Gents,
time after time after time this same question comes up. Yes car oils are cheaper, and from a lubrication point of view if you choose a good quality synthetic, they're more than up to the job BUT... and it's a biggie... there are two major issues:
1) all car oils are not designed for use with a wet clutch, and
2) there are no (or very few) meshing gears to chop up the carefully engineered molecules in a typical car engine.
So? Well, the wet clutch in a bike doesn't deal very well with some types of 'friction modifiers'. You may be lucky depending on the oil type you choose, but there's a high possibility you'll end up with a slipping clutch. When this happens the only solution is to replace the friction material. Mobil 1 is particulary excellent in this respect. Wonderful oil, but an almost guarantee that you'll need to rebuild the clutch after more than a few thousand miles (on road) or a few tens of hours of operation (off road).
The chopping up of those carefully engineered viscosity controlling molecules matters too... because you end up with something close to a straight viscosity grade pretty quickly when you're mashing things up with several sets of meshing gears and ball-races too. Usually not too much of a problem, but if you're using a wide multi grade oil like a 0W60 and you actually get the protection of a straight 20 grade, is this really what you want when you've paid all that money for a multi-grade???
Bike oils are significantly different, especially if you're considering fully synthetic 'high performance' oils, and they're more expensive as a consequence.
You could argue the change intervals on a dirt bike are sufficiently frequent for things to matter less and I think this is quite valid. You may well get away with the destruction of the multi-grade facility, but it causes me issue. I've direct experience of the clutch slip. It's cumulative in its affect. You may be lucky, but you may also be on borrowed time. A clutch is not hugely expensive to rebuild, but if you're trying to save on the running costs...
Alternatives? Choose a semi synthetic and change more freqently. If you're racing, you don't really have that option, so find an oil sponsor!
OK, this is my opinion. It's based on direct experience, on and off road. You've absolutely no obligation to follow it, but my advice is save your money elsewhere and avoid repeating my mistakes.
Cheers... P