If your sanitation is good, the pros greatly outweigh any cons (which are few and far between anyway). One of the 'pros' is not spending money for yeast every time you want to brew. A bigger 'pro' is the fact that repitching the yeast from a batch almost invariably results in a more robust fermentation (at least that's what I've observed). On top of that, it seems that after a few generations of healthy fermentations you end up with yeast that has entrained itself to your particular environment, and which can be repitched from batch to batch many times with only occasional reculturing new starters.
I actually selected my house strain more than 25 years ago by combining several strains (including one favorite that was passed along to me whose origins was unknown). I took that through more than 20 repitches, and was getting better results with each successive brew until I finally cultured up the "winner" (since ultimately, one strain will dominate) and wound up with a yeast that since the 1990s has never failed to give really great results across a wide variety of "styles". I'll still play around with other strains (I've become a huge fan of ECY's "Old Newark Ale" strain), but always wind up returning to the "winner" of my old 1980s experiment.
Experimentation is, in fact, one of the most fun and potentially rewarding parts of this hobby.