Speed is important on long routes. Many alpine routes are so big, that unless you are fast, you are going to get benighted. Trust me, there's a huge difference being six beers deep in the pub after finishing the climb and suffering a cold night somewhere high on the route.
Note that being fast is very different from hurrying things. The easiest way of shaving minutes and hours from the ascent time is to be efficient. After all, not doing unnecessary things and doing the necessary ones in an effective way does not require any additional energy (might actually save some). There are few recent blogposts giving excellent tips regarding the speed on big routes. Be sure to check also my earlier entry on the same thing: Multi-pitch efficiency.
All that said, it doesn't hurt to train. Hmm, bad choice of words; actually, if it doesn't you aren't doing enough of it. One of the more effective ways of training more is to make it so easy that you run out of excuses of not to. In this regard, home wall is a great. No I don't have one, but I probably should. Due to housing arrangements, it may be a challenge to build a wall anchored to walls. However, there's no reason why it would have to bolted on, it could just as well be free-standing. And if there's no room for any sort of climbing wall, plain old bar and possibly rock rings can fit into almost no space.