Speaking as an experienced shooter and competitor, yes the Professionals all shoot low, some horribly so. I have two, they both shot 12"+ low at 15 yards. The basic problem is the same with all the fixed sight .32 guns based .38/.357 frames without alteration. A fixed sight frame - if originally designed for .38 Special/.357 Magnum - needs a higher rear sight to target with the lightweight .32 bullets. But that would entail building an entirely separate frame line for .32 guns, and the limited market for those guns just doesn't jibe with profit maximization to create an entirely new frame production. So they all use the same frames they use for the .38/.357 guns.
The Ruger SP-101 fixed sight 3" gun in .327 Federal Magnum is afflicted with the same problem, and to correct it, Ruger puts a tiny nib of a front sight on it bring the POI up. It still shoots slightly low. If you changed to a hi-viz front sight, the gun shoots very low due to the higher front sight change. Some aftermarket SP-101 sights explicitly state "not for .32 guns".
A better way to handle this problem is make the .32 barrel with a slimmer contour, narrowing at the muzzle, so that a normal height front sight will sit lower, achieving the same result with a more visible front sight. Look at an old-school Colt Police Positive Special or S&W J frame .32 - the barrel is naturally slimmer at the muzzle due to the smaller calibre, and the front sight is quite good. But that is again too much extra work for the modern revolver manufacture, who wants to use the same barrel blank for everything, and just drill a smaller hole in the barrel for .32. This also conveniently appeals to the modern shooter who thinks a mild recoiling small-frame short-barrel .32 concealment gun needs a heavy barrel.
Charter used the same frame as the Bulldog on the .32 Professional. That would have been OK if they would have taken the 3" Classic Bulldog barrel and tapered it to the muzzle for .32. Instead, they installed a heavy barrel with a big rib on top, and then made it worse by adding a HUGE blob of a fiber optic front sight on the end of it. I'm assuming this was done to make it look cool and sell guns. This substantially raised the front sight height, subsequently pushed the POI way down.
In doing this, it would have been nice if they had spent an extra 50 cents to make a couple of small barrel cuts beveling the rear corners of the rib to match the existing unchanged frame bevel, instead of leaving a couple unsightly hanging square edges at the back of the barrel.
My first nitride Professional was so bad I returned it to Charter with test targets. They ended up sending me a new gun with an adjustable rear sight - kind of a custom one off. That zeros just fine. I figured maybe that was a fluke, so I bought a stainless one, and that shot low also.
At 7 yards, if you bottom the front fiber optic in the rear sight notch, the top of the front sight actually sits above the top of the rear sight notch. Using what is referred to today as the "combat sight picture" (that is, covering up your target with the front sight and expecting POI to be through the center of the front sight and not on top of it), you can get close enough to that particular POA for defensive shooting. Based on 34 years of LE experience as a firearms instructor, I think the current fad "combat sight picture" is a crock of dodo... but that is another issue.
I'm guessing they shot these guns during development and realized the problem and said to hell with it, it's too expensive to make a special frame just for these .32s, and 98% will not notice it.
I like Charter guns but agree the QC can be inconsistent. I bought the high polish Charter Undercover .38 and it is the nicest handling 5-shot snub in a long time. I carry it frequently and the trigger action and overall smoothness is FAR superior to any other Charter, and most S&W J frames I've handled out of the box. On the high polish guns, the junction of the grip/trigger guard assembly and the frame is rounded and polished, that is why they can sell it with the original style small grips. Every other charter has some kind of wrap-around grip because where the frame meets the separate backstrap, that is now left sharp and unblended for reasons of economy and will rip the web of your hand up in short order with serious loads. Look at the front of the muzzle on the outside edge - hey Charter how about spending 25 cents and put any kind of a bevel on that square edge on what is supposed to be a carry gun? Charter has cut corners on guns that were originally designed to be less-expensive to manufacture: not usually a good look or result. At least Charter doesn't rip the wallet off your butt to buy their guns.
Charter makes a 5-shot 2-1/2" barrel ".41 Mag Pug" on the "extra large frame" which is somewhat larger than the Bulldog - about the size of the old Ruger Security-Six cylinder. I bought one of these guns and while full house .41 Magnum rattles your teeth, the little Pug shoot very well and right on POA at 15 yards. I got a 1-1/2" group at that distance right on the money with the Remington Hog Hammer Barnes bullet load. I mostly handload .41 Special ammo for it at a more sedate level around 900 fps, which in the light gun is still something to behold. With Pachmayr grips this gun is about as light as you are going to get for a bigger-bore magnum. No complaints at all.
I also agree Charter will make whatever issue you have right. This is just the state of manufacturing generally today. It is less expensive for the factory to pay shipping both ways and repair (or more likely replace) a gun, than it is to spend the extra $$$ in the first place to properly inspect all guns at the factory and reject out the of spec guns ones. The vast majority of gun buyers either don't shoot their guns, or fire less than 50 rounds, and are not well skilled to begin with, so don't notice any problems. Occasionally a random low QC gun will get into the hands of someone that has a clue about they are doing, and it's cheaper for the manufacturer just to fix or replace that specimen. It has been a competitive market and price drives a lot of decisions. Unfortunately, you cannot make a decent revolver in the manner of a plastic framed pistol and have it either appealing or properly functional. But people don't want to pay for a functional quality revolver, when you can buy a plastic 9mm for $299.
I have seen the exact same philosophy at work at Ruger and S&W with revolvers, as I have sent plenty of those back as well. With the current S&W it is usually the low-margin grind-em-out J-frames (I completely gave up on M&P pistols after many disappointments), although I've sent Performance Center guns back that were Lack of Performance guns.
With Ruger it's everything and anything they make depending on the day of the week - the MSRP they charge for guns of Harbor Freight quality with horrible triggers, shaving sharp edges and gross finish flaws is appalling. I recently looked at high-polish SP-101 "Match Target" model that I needed double trigger fingers to cycle through double action... what kind of match is that gun for? Maybe a no-ammo pandemic pretend match. I can't wait to see how much quality Ruger can soak out of Marlin to bring it down to their level of disappointment - I'm guessing a cast receiver filled with MIM everything and clad in their crappy polymer stocks - with "through hardened bolt and hammer forged barrel", as if that would make the rest of it OK.
I've seen new Colt Pythons, Cobras and King Cobras that were an embarrassment, beyond the baked-in embarrassment that these guns are even when in spec.
There are no more craftsman at the major gun manufacturers, just parts assemblers. If it isn't moulded plastic, MIM or cast, slap-em-together parts - they just fall flat trying to produce something worthy of the close to $1000 they charge for most any steel revolver. S&W and Ruger have been trying to make a revolver with semi-to-unskilled labor for the past 10 years and it shows in the results. You can blame part of this on vulture capitalists buying up gun companies and ruining them.