Switching out of Rep and into PS does cost you a lot more beaker wise than US into PS.
The only issue is if you are a rushbuy economy then your low production cottage cities aren't gonna do anything more than keep from imploding under PS in a war weariness crisis. You won't really be gaining any advantage.
If you are a hammer based economy you can gain a huge advantage in military production when you need it on top of not losing war weariness citizens. If you need this advantage you trade off research for this or often In my case I shut down research production in such phases to save gold, pump some EP (always help tons in late wars for riots) and pump some culture into some new cities before I switch back toa peaceful economy.
With US not only do you not have the option to trade up (except through the slider), you have to suffer whatever war weariness comes your way. Which can force a culture slider increase (a lot bigger deal for a US economy to lose money in culture slider as it costs more and you lose productivity)
Ummm no, moving out of US costs one

which is worth no more than 3

for a direct rushbuy; less for Kremlin based uses. More tellingly a smaller proportion of your production comes from US driven

(thanks to corps, mines, mills, and WSs) than the percentage of science comes from rep

. In addition taking 5 happiness off the top is not without its own troubles for your larger cities. With a nice late game terminal economy, you can reach some insane maximums with FS cottages and corps; build or take the Kremlin and CR. Build the internet. You now can outproduce mines with cottages with a 3 building infrastructure base. You can use Rushbuy one turn to cash out gold in one unit per city fashion, and then swap back to PS for perpetual war.
Of course for the most efficient late game war you should be suffering essentially zero WW; nuke and win.
If you want EP, just pump FS cottages via the slider, it's the most effective way to get it. Late game drafting is handily inferior to late game whipping. Kremlin whipping Sushi is more efficient than drafting rifles; let alone infantry or mech inf. If I have the pop growth to regrow multiple pop drafts, I'm normally better off whipping out nukes, MA, MArty, bombers, etc. Late game drafting is pretty much a Spi/CR gambit that is useful only when your war plans hit a major snag.
As far as using the cultural slider, meh a few turns at 20% (which goes a long way all three buildings) is cheap to for a conquest. Even if we assume that 100% of your

is going to science, a 20% loss of

from fighting WW is less than the typical losses from losing rep

(as high as 50% of your :beakers: output, though 35% would be more typical).
To whit, US -> PS costs you some production, normally less than 20% of your total production and if you are that committed to a war (assuming this isn't just a swap of opportunity for a few turns); well over 80% of your production should be going to units . Swapping from rep to PS loses you around 50% of your science output; and has happiness costs, on the flip side you do gain more production. Alternatively, dropping down 20% culture is not the end of the game for cottages, you still have 5.6

+ 1

per tile overall yield; which can handily beat all other yields (mines/WS and farms gives 2.67

per net tile, simple conversion gives 2.87 equivalent

). Note I am assuming neither the Kremlin nor FIN here, either of which demonstrates even more dramatically how much more you lose going Rep -> PS than US -> PS or fighting it off with culture.