+1 If the tiles are 9" by 9", the are likely ACM (Asbestos Containing Materials). The tiles themselves are not the real issue because they are not very friable. The Mastic is the issue and caution should be taken when removing that as the previous poster mentioned. As a general rule, if the mastic is black, get it tested at a minimum.

I second what glennsfc said about no plywood. I would even be leary of using laminate. We used vinyl tiles on our floor (self-stick) 26 years ago. Then put an inexpensive area rug where the kids played (in front of the tv). That was so easy and bullet-proof with whatever the kids spilled. Arts, crafts, glue, it took so much abuse. Easy to change out the area rug every so often. When we laid the tile, we used a waterproofing film over the cement floor first before laying the tiles. Ours is a walkout basement. No water issues and I have only occasionally had to run a dehumidifier. (i.e. this summer only once) 26 yrs later the tiles are still down and I'm looking to replace them only because I'm tired of them but they are still stuck tight and will require some work to get them up. Tile is in the laundry room and bathroom down there also. We do have carpeting in a bedroom down there - just regular padding and carpeting. We have never had a mold or mildew issue. Never. You don't say if your HVAC system runs thru the basement? And do you ever need to use a dehumidifier down there?

We have hardwood on our main floor and LVP on our stairs down to the basement as well as on the basement floor (over cement). When the LVP was first installed on the stairs (it's been a little over a year now), my husband thought the "lip" part of the stair treads (the bull-nosed edge piece) was not installed perfectly flush and secure on several (I think 4) of the treads, so I wonder if that is not uncommon and is what your flooring contractor is worried about. I didn't even notice it, but my husband is a perfectionist and it bothered him. Rather than complain and have the installers come back to address the issue, my husband fixed the issue himself. I think he used tiny little nails (with no heads) to better secure the edge pieces to the adjoining LVP pieces, and I used dots of acrylic paint from my art supplies to cover the bitty nail holes. We have never had a problem with them since and we are up and down the stairs many times daily so they get heavy use. Just wanted to mention our experience in case that makes any difference for your decision. I don't regret using it on our stairs. We picked an LVP that coordinates pretty well with our upstairs hardwood in color, just a little more rustic which fits our basement vibe. We didn't want to introduce yet another type of flooring just for the stairs.

WPC is the preferred choice when selecting LVP flooring for your basement because it is softer and warmer compared to SPC. An 8mm thickness offers particular comfort, especially with a nice 1.5mm pad. If you desire an even better underfoot feel, I recommend using a firm cork composite underlayment beneath your WPC floor for added cushioning.