If, the tile installation is solid. You will need to install a self leveler designed to go over ceramic tile. You may need to abrade the glaze on the tile, depending on the SLC brand.

I am with MIllwork on this, remove it. Hammer and chisel, then grind off any leftover mortar.

I've laid wood over tile many, many times. I think it's a good idea, if you can meet all the necessary conditions. I assume that like most people these days, you'd be installing a reasonably wide engineered plank.

As millworkman mentions, you need to make sure it works with your elevations at doorways, adjacent floors, and at cabinets and appliances.

As G&S mentions, the tile needs to be sound and firmly adhered. Tap on it all over to see if it is sound. You can remove a piece to determine whether it's bonded properly

If the tile is smooth and flat, there is likely no need for leveling. If there are a few high spots, they can be chipped and filled. If you have a few loose tiles, they can be reglued or removed and filled, along with filling low spots. Abrading is a good idea, though I once glued wood over a slick shiny tile that tested positive for lead, so we were not allowed to abrade it. I highly recommend doing a bond test using the wood and adhesive specified (and a lead test for that matter).

On the last one I did, leaving the tile was a huge plus because when the house was added to, the new slab was higher than the old. Leaving the tile in part of the house not only saved the time, money and mess from removing it, but also saved on preparation costs.

The first time I did this I was very wary. The tile floor was abraded, primed and floated with Ardex, covered with a sheet vinyl moisture barrier, then covered with engineered plank. On the opposite end is the one I mentioned above, and a similar job where the floor was glued over the hideous rough brick pavers like you'd see on a driveway. Both jobs were in a condo, so we were able to leave the existing sound deadening in place, again saving money, time and mess.

Any installation of anything is only as good as the substrate below it. If that is broken, or has cracks, or is tenting, then that is an absolute NO. The biggest drawback is all of your baseboards will need to be pulled and reinstalled, or the wood will have to butt to it with an expansion gap, that shoe mold will have to cover. So your baseboard gets shorter, and you get shoe mold both. Then all of your door casings and doors have to be undercut, or the wood won't work. That's permanant. You can't change your mind later and rip it all up and scab on more door bottoms and casing bottoms. Not unless you want it to look 9 kinds of tackyhell. There's also the problem of you boxing in your DW or other appliances in the kitchen. BAD IDEA.

Thank you, everyone. All good points made here. In the long run would it be better to go with luxury vinyl???

NO. In the long run, it would be better to do it right, and remove the tile, address the subfloor remediation, and then do anything but temporary plastic floors.