Now, this is just a hypothesis, but playing the harder difficulties, rather then holding your hand, will kick you around and force you to learn how to play the game. Then you will be forced to get good and adopt effective tactics to progress. When you finally enter a multiplayer setting, you'll have all the experience of medium/hard mode behind you.

Or, you know, you can enjoy the game you bought.
One or the other :p

Of course, considering many of us don't play multiplayer...
You could just play however you like.
Plus, I imagine playing SP on hard is no test for MP anyway.

AI opponents are nothing like real players. You'll still be a noob.

I think it depends on the game personally, some use very different skillsets for single and multiplayer. Taking Left 4 Dead as an example, you can do fine in single player while completely ignoring the skills which are most useful in the multiplayer version - mostly communication based, but there's also the lack of any default way of learning the skills of the infected outside of multiplayer. Plus it doesn't prepare you for the thick skin you need to develop to play in pubs. Maybe they should make the bots yell at you in broken english and votekick you randomly.
Left 4 Dead may be a bit of an extreme example because the single player mode is so neutured though. But I think the example holds on some level for most multiplayer games with single player campaigns, you're going to get destroyed when you first step into multi unless you get it at launch and jump into multiplayer straight away.

Outside your idea that all things multiplayer are an FPS... thats not true. Ever played RTS? Civilization games with the hardest computer are brutal, same with Total War. Tough TOUGH NPC's that test your intellect and your patience. Thats something I much prefer over seeing how fast I can move my crosshair over some guys head and clicking.
Age of Empires? Ouch, but man is it fun. With certain genres, you don't need real players to have fun. Thats why I don't like online FPS'. Campaign, sure, but multiplayer is a real bore to me.

I find that most FPS, Racing, Survival Horror, Platforming, Shmup games are easy now that I automatically choose the hardest difficulty.
I remember playing CoD2 and blowing through the singleplayer, only to have someone in multiplayer ask me how long it took me to beat the game on expert and tell me how impossible it was. I was amazing at the multiplayer by the way, I remember lobbing grenades over buildings to frag the enemy with our flag right before they reach theirs...returning the flag and then grabbings theirs for the win no scoping everyone the whole way back. The whole stats and extra abilities ruined the series. :(

Some of us play games for fun and killing time, more than to learn to master it and beat others into the ground at it.
I always play normal. If it gets frustrating I might set it to easy if possible, if not, I'll look at a walkthrough online and if it looks like it's going to be too much of a hassle (force me to repeat myself over and over again until I beat it) I'll get frustrated. Last thing I do before uninstalling is reading a bit on what I'll be missing. If It's more of the same, it's bye bye from my hard drive.

Play Soldiers: Heroes of World War 2 on the hardest difficulty. You'll go back to "Easy" after crying compulsively.
As for me, I'm with Gundato - I play games for fun, not to be "3l337". Not that I don't enjoy a challenge sometimes - I just don't like challenge when it keeps me from having fun.

I play games for entertainment and story. I don't have any interest in struggling through a game just so I can flaunt my e-peen.
The same applies to multiplayer games. I just play for fun, if I do poorly I don't really care. I do try to be somewhat decent on MP though because losing all the time isn't much fun.
But I usually play on the normal difficulty, if a game is exceptionally hard for me I'll turn it down. On my first play through of Dragon Age I had to play through on Easy. I started my second run on Normal, but I haven't played it in a while; should get back to it.

I always play on normal, then if I feel like playing through again I go on to the hardest difficulty. If you want to get good at multiplayer, play multiplayer... Take HL2: Deathmatch for example (in my experience). I first played HL2 on Easy, went on multiplayer and slowly became some sort of god with the Magnum. 'Course, i'd probably be shite now. :P

It depends drastically on what the difficulty levels do, if its just buff/debuff for hit points or weapon damage or something then you really don't learn any less by having it on moron, easy, medium, hard, insane or omgwtfbbq because the mechanics are the same.
A friend and I were talking about an ideal difficulty option the other day, instead of making things easier or harder with hitpoints, a game could give you more to do. We were thinking that in splinter cell on easy you have to hack a computer to get data but on medium or above you trigger an intrusion alert and have to quickly run over to the comms room with the firewall (picking or smashing the lock) to disengage it before it can broadcast the alert

I only play on highest difficulty now. I used to play on normal in the late 90s but always felt like I was missing out on something.
Medal of Honor: Allied Assault on the highest difficulty setting is extremely challenging, particularly in the final level when you have to escape the bunker while wearing a gas mask, being shot at constantly and a ball of fire is racing toward the open air right behind you. Then getting out as the place comes down and evading the final wave of Waffen SS as you race for the train leaving, with or without you..

When I was younger and had more time, I was more of a skill focused player and was competitive. I even have the VIP pass to the Nintendo World Championships to prove it.
However, now I have more games than time, so I've become more of a gaming tourist. I sample lots of games, but master few. I still have too much pride to play on easy, but I don't feel like I need to become a gaming master for any particular game. I don't even feel obliged to beat each game I buy. Sometimes, I'll just enjoy it for a few hours and move on to something else with the hope that I might one day get back to the old game. The hardest difficulty level can really put a monkey wrench in the gaming tourist philosophy.