A chronograph tells you nothing about chamber pressure, so it has no bearing on how close to maximum I go with a load.
I strongly disagree. Pressure and velocity go hand in hand. A chronograph won't tell you the exact chamber pressure, but it is the best way to get a close approximation without expensive equipment.
The brass and primers tell me what I need to know about what is safe and what isn't.
Visible brass and primer issues don't even show up in rifles until you reach 70,000 PSI, which is WAY over pressure. This is the LEAST reliable way to predict pressure. Primers can also crater with loads well below max. That will depend on the exact primer used and the bolt face and firing pin on your individual rifle.
Loading near max loads without a chronograph is like driving a car without a speedometer on a road with a 70 mph speed limit; just an alarm that sounds when you reach 100 mph.
If your load manual says that 40 gr of powder under a 100 gr bullet @ 3000 fps is a max load and will generate 55,000 PSI then you can be pretty sure that if you're getting 3100 fps with 40 gr powder that you are OVER 55,000 PSI. No you won't know the exact pressure, but if you are waiting on flattened primers to show up that won't happen until you reach 70,000 PSI.
You also have to account for different rifles and different barrel lengths. If the data in the load manual is from a 24" barrel, and I have a 20" barrel then I'd have to consider this. Depending on the cartridge I'd probably consider 2900 fps, maybe less, as the max load instead of 3000 fps. In some rifles you might reach 3000 fps at 38.5 or 39 gr powder instead of 40. If that were the case then I'd consider that powder charge as the max safe load in that rifle. In another rifle you may not reach 3000 fps until you get 40.5 or 41 gr of powder. I don't advise doing that however. While it may be safe in one individual rifle, it may not be in another.
My goal is to produce sub MOA groups at the fastest safe speed. I use my chrono to measure speeds to let me know when I'm approaching being over pressure. Most of the time I find the speeds I get are very close to the predicted speeds in the manuals. Taking into account barrel length, and differences in individual rifles. Most of the time I end up getting the accuracy I want anywhere from 1 gr under to 1/2 gr over what the book says is max, but none of my speeds exceed what the manual says is a max load.
Only once, with one rifle, using one powder did I run into a problem. I was well under a max load so I went up 1/2 gr. This load was still supposed to be well under a max load, but my velocity jumped considerably and I was nearly 100 fps faster than I should have been even with a max load. And I was still 1.5 gr under that. There were no primer or brass issues yet, but I was clearly overloaded with that combo. I switched powders and found what I was looking for at safe pressures.
That one incident paid for my chronograph and convinced me of their value. I could have easily stopped at 1.5 gr under what the manuals said was a max load and still been over pressure without knowing it. With every other rifle and load I've ever used I could have taken the load data from the manual, worked up to a max load and been perfectly safe. But I would have had no way to know for sure that it was safe without the chronograph. Priced at, or under $100 having one offers peace of mind that is well worth the expense in my opinion.
Being able to calculate trajectories is nice, but secondary in my view.