Note: Much of this material, and more, is also covered in answers to the question: Can you fly a light GA airplane into a major hub? (Didn't know that at the time I wrote this answer.)
Landing at higher than normal speed is not recommended.
Tricycle gear airplanes require a nose-high attitude on touchdown in order to ensure the main gear touch down first. The nose gear is not designed to support initial touchdown forces. In many typical small planes, forcing the plane onto the ground at too high a speed will strike the nose wheel first, risking a collapse or prop strike.
At high speed, the control surfaces and wings are still capable of producing significant aerodynamic forces. If you've forced your wheels onto the ground, you may be producing a lot of torque with the elevator, again, risking gear collapse.
Kinetic energy is proportional to the square of your velocity. And crash damage -- both to the airplane and to its passengers -- is proportional to energy. If you do collapse the gear or lose control, you're going to have a lot more energy to dissipate. And if that energy is dissipated by your body, it's going to hurt. A lot.
You might overheat your brakes, causing brake pad/rotor damage or even a fire (I'm aware of at least one instance of a Piper Cherokee catching on fire because the pilot attempted to take off with a half-stuck parking brake.)
It is true that you will sometimes be pressured by controllers at large airports to keep your speed up as much as possible on approach. It's hard for them to sequence you when you're only flying half as fast as the guys in front of and behind you. The important thing to remember is that this is their problem, not yours. There's no FAR that says you must hot dog your airplane in order to fit in with the big boys.
Here are some things you can do safely to make everyone's job easier when operating at large/busy airports:
Practice your controlled-airport/airspace proficiency.
- Know, and use, standard ATC phraseology.
- Listen carefully for your callsign. Don't make them repeat themseleves.
- Have a plan in advance, know what you want, and make sure you communicate that to them clearly.
Have the airport diagram handy, and study it before the flight so you know where you'll be taxiing and won't mess up ground operations. Ideally you should be able to taxi on your own, but if you're not comfortable when you get your taxi instructions, request a progressive taxi.
Know your airplane and its capabilities. Fly your approach at the highest practical speed, but no faster. Know how fast you can go on a 3 mile final in order to be able to decelerate to normal short-final and touchdown speeds.
If you're not comfortable with your proficiency in these areas, consider getting some more practice before attempting a flight to a "major" airport. Or, bring a CFI along with you who can help you out and give you pointers.
The bottom line is under no circumstances should you compromise safety in order to please ATC or the airline pilot behind you. As long as you are proficient and do your best to accomodate ATC's requests within the safe capabilities of your airplane, you'll do just fine. (In fact, I've found controllers at major airports to often be very pleasant to work with.)