First, MOST "small" home-style compressors are oilless, so that won't be the problem. (Larger ones are oil-lubricated)
However, those compressors only put out 100-150 psi typically, which is nowhere near enough. You need 3000 psi to charge an AL80, and more for HP steels (3500 or so)
A small "home usable" dive compressor will run you $2500 or so, runs on 240V (requires a 240V outlet or direct wiring) and, as was noted, also requires filters which must be changed on a regular basis - while they're not stupid expensive, they're not cheap either. If you decide you want one, I personally believe that the Alkin W31 is the "best value" in the small compressor market, all things considered. (If you're looking for something larger, in the ~5cfm range, then you need to seriously consider the Coltri-based Max-Air 55 series and the Bauer Oceanus or Capitano, both of which are very nice and a bit cheaper than what Alkin has in THAT size range.)
Neglect maintenance on said "home compressor" and you will get a lung-full of oil or (at least as bad) CO, which can KILL you.
IF you dive Nitrox AND live where fills are expensive (more than $6-7 a bottle for Nitrox) then it can be worth it, IF you dive a lot, to put in your own fillstation. I dive perhaps 200 bottles of gas a year between myself and a buddy, so for me, at least, its pretty simple on the math - I have a $2,000 annual gas bill if I buy my gas. In two years or so I pay for the hardware and maintenance - so for me, its worth it.
But for those who dive infrequently, or dive only air, its almost certainly NOT worth it.
If you are not anal about doing the required maintenance, its downright dangerous to do your own.