I personally would have concern if I were reloading without a chronograph.
And, yes, others are right in that if you're not pushing the envelope you're likely fine.
But I want to know how my handloads compare to factory ammo as a baseline, as well as using it to figure out new loads with powders and bullets for which load information doesn't exist. And depending on often-inconclusive "pressure signs" as a way of identifying a too-hot load doesn't excite me much.
I'm trained as a scientist; measurement is paramount for doing science well. If I can't measure how well or poorly my loads are doing, both in terms of velocity as well as consistency, well, I'm not comfortable.
Here's a good example of why I use one. I've been trying to work up a load for 147gr XTP rounds for my 9mm. I found some loads for Universal (one powder I have on hand), that max at 3.4 grains. Worked up to that load and shot them through the chronograph.
I was trying to achieve something similar to commercial SD ammo using that bullet, which is advertised at 975fps and with which I've seen people get over 1000fps.
I averaged about 870 fps with my loads, which doesn't even come close. If I just loaded them and shot w/o a chrono, what would I know? Accuracy, sure, but if it's a mouse-fart load, it's not an effective load, and you can't tell without being able to measure accurately.
Chronos are cheap; I have the Competition Electronics ProChono; cost me under $100. If I had to do it over again, I'd get one with a printer and remote control, but the budget at the time could afford $100.
A tip I can't take credit for:
I read this elsewhere on THR, but someone suggested using wooden dowels instead of the metal rods for holding up the diffuser screens--just in case one missed and shot a rod, wrecking the chrono. I bought a couple of 3/16" hardwood dowels, and with just a bit of sanding of the ends after I cut them, have wooden diffuser rods instead of metal ones. Very clever and congrats to whomever though of it first.