It certainly is!
I spent 7,500$ on a Playstation 3 just to play the games asap.
The truth tho is that if it is a game you really like 3,000$, while a lot of money is probably an acceptable expenditure. The Sims, Warcraft, Final Fantasy Online etc etc are games that offer a nearly unlimited amount of playtime, and they are always available at the click of a mounse.
3,000$ might be a little too much if you intended to play the game casually, but if you are going to sink the kind of hours into it that I have sunk into Warcraft or Guild Wars, then it is probably cheaper when divided by the actual hours played than a daily cup of coffee.
More importantly, you are not really paying 3,000$ for the game, you are paying it out for the computer. Once you purchase the computer you have gained an asset. You will be all set and ready to go when the next Sims game or other software that appeals to you hits the stands.
Or if you eventually tire of the Sims and can't find anything else out there to sate your wont for gaming you can sell the computer for some kind of return on your investment.
No matter what kind of advice I or anyone else gives you, one of the main factors is , of course, whether or not it is acceptable in your current budget. Be aware that there are a LOT of "get the PC now and pay for several years" programs out there, most of them charge high interest, but it is an option.
Money SHOULD be spent when it is necessary, and if gaming is a hobby then by all means, FEED YOUR NEED!
Good Luck !