Not required if you are staying within published data.
I strongly disagree. Think of a chronograph like the speedometer on your car. If you stay close to beginning level loads it might not be necessary, but why would someone buy a 30-06 and load it to just over 30-30 speeds. Like people who drive 35 in a 55 just to be safe they don't speed.
When you look at load data you may see a load that says 47 gr of powder "X" is a max load with 150 gr bullets and to expect 2900 fps. The 2900 fps is the limiting factor, not 47 gr of powder. When working up a new load you start at a lower number, maybe 44 gr and work up to 47. But it is good to shoot them over a chronograph as you go. When you start approaching 2900 fps you are approaching a max load.
You may reach 2900 fps in YOUR rifle at only 45 gr. Then 45 gr is a max load in THAT rifle. In other rifles you may go all the way to 47 gr and still only get 2800 fps. Technically it would be safe to go over 47 gr until you reach 2900 fps in THAT rifle. But I don't advise going over book loads. While they may be safe in one particular rifle if they somehow ended up in another rifle could be way over a max load in that rifle.
Most cartridges max pressure is 60,000 PSI or less. Traditional pressure signs that people look for don't even start showing up until you hit 70,000 PSI. Yea, people loaded without one for years. Some of them were shooting mouse fart loads from their rifles, others were well over max loads. But both groups were blissfully ignorant of what they were doing.
A usable chronograph can be bought for less than the cost of 2 boxes of premium factory loads. If I had to spend $400-$500 for one I might be hesitant. But as cheap as they are today no hand loader should be without one.