I remember examples of round-trip ticket A-B-A costing $x in A, $x/2 in B (plus another fare for country C) for some city pairs, but I don't think this has really been a thing in a decade at least.
Personally I mostly use Google Flights for flight search (or seats.aero for award travel search) and booking.com for hotel search, and then book directly. I've booked probably 100+ hotels through booking.com and then quit entirely after hitting that long tail bad experience.
[1]: I'm a few years out of date on this and don't know the current legalities, but major OTAs (Booking.com and Expedia, who control probably 80-90% of third party hotel bookings) used to have a "most favored nation" clause that prevented hotels from advertising lower prices through other channels without a previous commercial relationship. Signing up for a loyalty program qualifies, so being logged in for direct hotel bookings can sometimes get you cheaper room rates. (In the US, things like AARP and AAA memberships also work.) I know the EU was pushing back on these clauses but I'm not clear on what the current state of things is.
OTAs can play "member" pricing games too I think so there's even better deals to be had.
So you definitely need to comparison shop, I make my agent take the pricing from all the OTAs and calculate a post-rebate price, then pick the lowest one.
Amex/Chase/Cap1 portals are still not worth it.
Even after the 5-10% cash back on hotels booked on their portal, you are still overpaying by 1-3% of the “book direct with hotel” rate.
Then once you take into account a 2-3% straight cash back card, the credit card travel portals tend to overcharge you by 5-8%. This is after taking into account all the points game nonsense. Do the math yourself.
This hasn't been my experience. I usually search through Booking.com and when I contacted the hotel directly, found that the direct rate is higher than the booking.com rate.
Just a thought but I guess if the airline web services were overwhelmed with noise, they wouldn't be able to do such price adjustments reliably. The only risk is that this might bump the prices for everyone and it will turn out that consumers are not price sensitive enough to force airlines to not do this.
What percentage of the total value is typically saved by those who check different devices, browsers, etc?