Two disadvantages I've seen to this while working for this sort of beast (in my case 3 friends bought out the last founder of a fairly old engineering services company and as part of the plan one of them ran a subsidiary that was essentially a startup):

As others have mentioned in other topics, you lose a filtering function. When the company evaluates your idea(s), their opinion will be contaminated with their presumed desire to keep you. They will also evaluate you as a potential startup founder but from what you say there's no reason to believe they're any good at that (and the skills required are different and quite a bit beyond consulting).

You'll have a safety net. Sounds nice, but it can become a dangerous crutch.