There is a characteristic called ampacity that is defined as
the maximum current, in amperes, that a conductor can carry continuously under the conditions of use without exceeding its temperature rating.
This all comes from the power equation you gave,
$$
P = IV \\
$$
and from Ohm's law:
$$
V = IR \\
$$
which lets you substitute the voltage in the power equation to get:
$$
P = I^2R \\
$$
This form is used to explain the "I-squared R losses" where input power is "consumed" by wiring. Usually it's used for power transmission lines, and this is also why high voltage power lines ARE high voltage - if you can crank voltage up really, really high then you get current to be really, really low for the same power, and then lower current means lower resistive losses in the transmission cables.
So in your case it doesn't really matter what the power rating is for the devices because electrical power doesn't generate heat, current generates heat (by the $I^2R$ losses described above).
I will concede that it's very frustrating to need higher-current ratings on low-voltage devices, because those aren't common use cases and so there aren't many (low cost) options available.
When I search on Digikey (no affiliation) and sort by price for disconnect switches rated >45 A, the least expensive option looks to be about \$25.
You could of course just use something as a switch and hope it doesn't melt, but if that's the approach you're going to take then the very best option would be to use a fuse that's rated slightly lower than your switch rating.
Let's assume you think all servos being stalled is so unlikely that you're willing to replace the fuse if that happens. How many stalled servos would this is a reasonable expectation? If you consider three stalled servos and three at max current, then you wind up with $(9*2.5 + 9*0.9) = 30.6A$ as your current rating. This still isn't getting you any cheaper results on Digikey.
Let's try to think more about your use case. If it's a hexapod (six legs) then maybe only three legs are in motion at a time while the other three legs are supporting the body.
So what if we assume two legs are stalled (six servos at 2.5A), one leg is at max nominal current (three servos at 900 mA) and the other three legs are at the minimum nominal current (nine servos at 500 mA). This now gets you down to 22.2 amps.
Still no good-looking options, so finally one stalled leg, two at max nominal, three at idle. This is $(3*2.5 + 6*0.9 + 9*0.5) = 17.4 A$. Now that the maximum current is less than 21 amps you can look at rocker switches instead of the power disconnect switches, and in that class of switch the cheapest option stocked by Digikey is $3.92.
That switch is rated at 20 A. As discussed above, the "one stalled leg" scenario would be pulling ~17.4 A. The switch is rated to 20 A, so you should be looking at a fuse that's rated higher than your use-case (17.4 A) but lower than your switch rating (20 A). If you can find a fuse rated for 18 or 19 amps then you should be able to operate in the one stalled leg scenario but anything more than that would blow the fuse, ensuring the switch contacts don't melt.
Looking again at Digikey you could get a fuse holder rated to 20 amps for \$1.51 and an 18 amp fast-blow fuse for \$1.88. Be sure to buy spares just in case!
If you find the fuse is blowing frequently then the "one stalled leg" use case is too restrictive and you need to re-evaluate the components you're using.
Remember that current ratings apply to everything in the circuit, notably also the wiring and electrical connectors you're using (spade connectors, etc.) Your fusing should be setup to protect the item with the lowest current rating, and the fuse should be lower than the lowest current rating.
