I can think of several reasons why this might not be the best idea for your game vs using an in game only coin
1) Inability to grant game credit. If your users play a lot, bring their friends etc you might want to give them more credit. If you are using bitcoin then those have to come from somewhere, or you can't do it. This will limit your ability to manage the ecosystem of your game in the ways that you might want to.
2) Supply Shock: You may find that when the price of bitcoin vs the dollar goes up or down then your game will be affected by money streaming in or out. If your game is presumably a business that has to run as one that might be a risk you don't want to take.
3) Data Security. If you have 10,000,00 games coins on your system there is very little reason for someone to try and steal them. If you have $10,000,000
worth of bitcoin then there are major reasons that someone might want to hack in and steal those.
4) Tax law. Depending on where you and your players are there may be tax implications. Or other legal regulations that you might run across. The last thing that you need is for the FBI to decide to check if someone is using your game for money laundering.