I play my bass on strap all the time (if I am taking it seriously). If I'm just grabbing it for a quick few notes I may opt out of strapping - but otherwise I've learned that strapping it on so that it's in playing position whether standing or sitting makes a lot of sense.
Regarding neck dive; I hate it and prefer to play an instrument that stays in playing position without requiring any support from either hand. Now that's an ideal situation and I agree that a small amount of neck 'dip' is OK since it can easily be compensated for with a good strap.
But I also feel that learning to play 'against' the instrument is far less appealing than playing with it.
There are ways to mitigate it for some instruments that dive. Lighter hardware, moving strap buttons, thick suede straps - as many have mentioned. But some instruments are going to dive no matter what. For me, that equals fail. For others, not so much. To each his/her own.
