On centerstands...
These seem pretty solid and sturdy to me. I haven't seen anything about them breaking. I will say that since I totally disassembled, cleaned, and lubed mine that it goes up and comes down much more easily. In fact, the first time I put it up after reassembly I applied the pressure I was accustomed to and I thought I was going to throw the bike over backwards.
It seems to me that a well-serviced stand would be a good place to start - then think about technique.
As for technique - I've been putting mine on (and off) the centerstand on a bike lift - where I do not have room to be on the bike. to get it down, I stand on the LH side, grip the LH bar and the lift handle, nudge it forward and pull it a little bit towards me.
Thanks for the alert on the potential for the grip to slide off the handle.
On sidestands...
The lean angle sometimes makes me nervous, but I do use it for short term rests. I rather like it when I have to park on uneven surfaces and can orient the bike to lean a bit uphill - then it stands up like a bike on a sidestand is "supposed" to.