And in case of carrier based ops using CATOBAR config Horizontal speed during the landing is critical .
not only the sink rates infact the approach speed during landing itself has to be higher so that aircraft can take off un-assisted in case the tail hook misses the arrestor wire .Also the tyre pressure for carrier based aircraft is pretty low as compared to their land based counterparts .
Lets look at the basics here. You need less horizontal speed while landing because you need to be able to brake and stop before you run out of runway. For a given braking capacity, the momentum you carry when you are landing has to be less than what the brakes can stop!.
Now for carrier landings, you have a very very small runway aka deck , indeed
. So to assist you in landing, the arrestor mechanisms will be rated for certain max loads (aka momentum , ie m*v) , which can bring a plane to halt within the specifed distance. There are limits everywhere , including the max deceleration the airplane can handle , the max the pilots can withstand, the optimum for long term life of the structure etc..
If you are landing a biggie like a EC2C hawker on a carrier, you need to come in really slow so that the total momentum carried is less than what the arrestors can handle. You will even dump excess weight if your momentum is higher than what the wires can handle at approach speed.
Now for a fighter, which is lighter than the EC2C , you can come in faster because you can carry more momentum , and anyway, the fighters have a higher stall speed than the EC2C and will stall if they come in as slow as the Hawkeye.So theoretically, yes, as long as you are within the arrestor's capacity, you can come in fast, but your deceleration will be violent!
From what I know, the arrestor gear brake capacity is adjust for each plane. You dont apply full potential to every plane, but is tailored so that max deceleration is not exceeded and the plane comes to a relatively gentle stop.
All the same, you cannot come below a minimum because the plane still needs to be flying when it hits the deck and not stalled and maybe take off again if it misses a wire!. So yes, the lesser your flying approach speed, the better it is (given the deceleration limits, the max capacity of the arrestor etc). Notice, the basics is not very different from landing on an airfield. You fly in faster, you need to apply more brakes, decelerate more to stop within runway length, than you would if you came in slower!. The wire is just a massive booster assisted power brake. That is all.
Lower tyre pressures have higher rolling resistance. But that again is not really important here for this reason (lower pressure tyres have better springing and shock absorbing capabilities than high pressure ones, so load on struts and undercarriage will be less). The plane is above stall speed when it hits the deck and with the engines on at full power, there will be no problem in taking off again.