Protoss have ability to be aggressive in TvP. MC and Squirtle show this constantly. Most protoss choose not to because it's incredibly risky for a race that has observers to be doing daft blink stalker/sentry prism timings or whatever silly shit MC is up to.
The problem that a lot of Protoss have is they struggle (in PvT anyway) to harass whilst macroing. They can do a few pressures or funky builds but when medivacs and stim finishes they more often then not are on the backfoot and have to wait it out. And that's fine I think, that's just how Starcraft works. There are times when one player can do shit and the other player has to chill the **** out until he can do something.
Lategame TvP is ******* annoying as hell though as Terran a lot of the time. I constantly get demolished by Protosses that I have huge economic leads against, and if you have an upgrade advantage/parity at some point well you don't really cuz of chronoboost. If you're floating shitloads of minerals well your mineral dump unit gets murdered by storm/colossus whereas theirs can actually take a punch so that's fun too. And yes the 30 warpgate dynamic is super awesome. I dunno it's tricky.
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