On an old laptop I think it makes tons of sense, and I've done it before. A Toshiba Qosmio with a Core 2 Duo 8000 series (I forget the exact model) and a 9800GT mobile. Made a ton of difference because the old paste had dried out and wasn't effectively cooling anything.
With new stuff I usually just use it as it is out of the box until that configuration becomes a problem. The one exception was a Compaq I got from Walmart with an entry-level socketed AMD CPU that I immediately replaced with a much fancier model of the same family shortly after purchasing. The cost savings was worthwhile in that case.
These days I think it's interesting that boutique notebook vendors offer to upgrade the paste for a $40-ish fee. Disassembling laptops can be (depending on the model) a rather non-trivial task. My wife's current laptop is a Lenovo Ideapad 330s that was hard to get apart. Had to use an iFixit spudger after removing screws because the lip was clipped all the way around. I only did that to replace the spinning rust with an SSD, but didn't mess with the cooling system.
edit: That's especially true when on at least some models, the CPU temperature (and thereby the thermal paste application) isn't a limiting factor. I just spent some time with the current-gen ThinkPad X1 Carbon, and CPU speed behavior was interesting
, to say the least. Eventually CPU temps dropped down into the 70s as the CPU clock got lower and lower, and so that made me think something else is responsible. Unfortunately HWMonitor wouldn't tell me anything about VRM temps, but that's my guess for the culprit, not the CPU.