Yes, the LOS guy opposite the chains (could be the L or H, depending on crew size, and which half of the game) needs to make judgments on reasonably certain first downs, or short, and give appropriate notification to the R, verbally, via hand signals, with O2O, or a combination of any of those. If it too close for him to make a reasonably accurate judgment, fine. Let the R know that it is close, and the R will move to the spot and take a quick look to confirm if he needs a measurement, or signal first down, or short (and next down).
My L does a fairly good job of that, but I have asked him to be a bit quicker and more definitive about those close situations. If a first, great. Stop the clock and give me a clear, but not demonstrative, signal. If short, give a timely and "big" dead-ball signal, followed by the next down signal, with a clear verbal notification. If short, just use the dead-ball signal, but with a strong verbal signal to notify me that it is close, and I need to take a look.
We have had three measurements, so far this season. Two were what I call "PR" measurements, just to make the teams and spectators happy, even though the result was reasonably clear to us. One was legitimately too close to call from far across the field.
Yes, we try to put the ball on a line when there is a new series at the end of a run, as often as practical. But, you can't always do that. So, yes, we do have measurements.