If you use wheat flour you will change the flavour and also add a slight graininess as the flour grains don't completely homogenise.
Adding corn/rice starch is advised by some Italian chefs too cause it's just a lot easier to get a reliable result (see the videos on Italia Squisita by Monosilio).
You can eyeball it with pasta water, it's just harder.
E.g. continuously stirring the pasta while you could be doing something is a waste of time where you could be doing something else, so less "efficient". Turning off the heating and letting the water cook covered uses very little energy but takes more real time so also less "efficient" in a way.
More active stirring also tends to break up the pasta, so depending on what kind you use you may end up with a different outcome (works great for pasta e ceci or pasta e fagioli! Wouldn't want it for spaghettini)
Mostly, I think the traditional way seems unnecessary because modern pasta is a lot stronger than it used to be. I you try to make a one pot pasta with low quality pasta (low protein) you may end up with glue (source: am Italian, live in country which produces shitty pasta).
As for the stirring, I'd say "it depends". Personally, I prefer to use fresh egg pasta. It cooks in maybe 2-3min and does require maybe 1min of stirring (maybe 20-30s in the beginning and end and perhaps one or two quick checks in between). I'm fairly sure I'd stir it somewhat of I used more water and I'd definitely need to strain it, so there the amount of time / effort is at worst the same, at best slightly in favor of using "risotto" method.
When it comes to dry pasta, I guess it depends on volume. If You're cooking a batch for 10, the traditional method probably makes sense. Otherwise, I pay attention anyway to how much the pasta sticks and clumps together.
the traditional way to cook cacio e pepe and the other recipes I mentioned in my GP comment is to move the pasta from the pot to the pan, then add some of the water from the pot to the pan so you have the "risottare" phase (most people in Italy would call that mantecare, at least in central Italy). I appreciate that adding something like corn starch would make it thicker, but also different people may have a different understanding of the concept of "creamy".
Risottare is cooking the pasta in little water (or other liquid) so all the starch stays in the pan/pot, adding water or sauce as needed. This is the part you do with broth when cooking rice for risotto.
Mantecare is when you mix the pre-cooked pasta with condiment in a pan, possibly adding some pasta water. This is the part you do with butter and parmigiano when making risotto ("mantecare" comes from "manteca", spanish for cream/butter).
You can do one, none, or both for a given dish, and get different outcomes :)
See e.g. (in italian) https://www.dissapore.com/cucina/come-risottare-la-pasta/
[1] I know you can verb anything, but this just doesn't work.
That said, as you mention, it's just a lot easier to get the consistency right by adding your own starch in measured proportions.
even famous italian pasta restaurants use the cornflour technique.