There are many myths about Concrete and automotive things. Now. many of these used to be true say 60 years ago but there have been major improvements in both tires and batteries and concrete for that matter.
IT won't hurt to park on a barrier.. Lynx Levers would be my choice since you need 'em anyway. but wood, Horse stall pads.. Or just park on the concrete.
Your tires, barring injury or under inflation, or over inflation or other problems shoudl last about 7-10 years. perhaps a bit less if they spend a long time in storage (Storage is bad for the tires no matter what they are on Suspended them in air it's bad for 'em. they like to be rollign, rolling, rolling down teh highway).