I've used a chronograph for about the last 20 years.
Getting consistent results requires you to understand how it works and to set it up properly - far enough in front of the muzzle, and on a stable enough tripod or support to prevent it from getting moved around by muzzle blast, and properly aligned so that the bullet goes across the center of each sensor, rather than angling across them (which increases distance and results in a low velocity error).
A properly set up chronograph will allow you to determine average velocity as well as the extreme spread in velocity and the standard deviation in velocity. Roughly speaking the extreme spread will be covered by +/- 3 SD in velocity, so a load with an SD of 10 fps will have an extreme spread of about 60 fps, while a load with an SD of 30 fps will have an extreme spread of about 180 fps.
The increased consistency of a low SD load is an asset to longer range accuracy, as the trajectories of each bullet will be more consistent at longer range. Those differences however won't often show up on a 100 yard target however, so having the velocity data is a great qualitative measure. In effect, if I have two loads of similar velocity that both give me a total of three five shot 3/4 MOA groups at 100 yards, but one load has an SD of 12 fps for the 15 shot total and the other has an SD of 26 fps, I'll take the 12 fps load. In fact, I'd take the 12 fps load even if it was slightly less accurate and tweak the powder charge slightly to see if I can find a slightly more accurate velocity.
That's another area where a chronograph can help. Most rifles will have a sweet spot in velocity for a particular bullet weight and style due to the harmonics of the barrel as it vibrates during firing. Doing a ladder test across a wide range in velocity will help you identify more accurate loads, but with a chronograph you can see the velocities where those accuracy nodes occur. Once you know that, finding that sweet spot (or sweet spots) with another powder is much more straight forward.
A chronograph will also highlight differences in primers. for example, in general I've noted that a WSR primer will yield a slightly higher velocity and a much larger SD in an accurate load in a small cartridge than a CCI 400 primer.
It will allow you to quantify the effects of different head stamps in brass. The .22 Hornet for example has a wide range of internal volume based on brand with Hornady being on the low end of the range, and Remington being on the high end, with higher and lower velocities respectively. Having a chronograph will allow you to tailor the loads to give the same velocity across different head stamps.
If you are a long range precision rifle shooter, knowing the mean velocity and the SD are critical to increasing the probability of a first round hit, as well as "truing up" your ballistic calculator results. Even if you are a casual hunter, you need good velocity data to get meaningful results out of a ballistic table, calculator or app.
Perhaps most importantly, a chronograph will help you determine that the load is doing what it is supposed to do. If you are getting wildly different than expected results, than you need to suspect and look for the cause.
Monitoring trends in SD can tell you when you've reached an upper or lower limit. For example, pressure spikes can be a problem with some powders in reduced loads, and as you reduce the load you'll see a sharp increase in SD in your chronograph data. In some cases, you'll also see an increase in SD as you increase the load beyond a certain point, due to the effects of decreased efficiency in a given barrel length or issues with the pressure curve.
It will also tell you about individual differences in firearms. For example, a PP series pistol in either .32 ACP or .380 ACP has tighter chamber than the FEG AP and APK series pistols (which are based on the PP series), resulting in a velocity difference of about 50 fps.