Hard to tell. Are those vinyl tiles still stuck to floor? On a slab or wood subfloor?

My contractor said leveling compound does not always stay intact...do not know if that is true or not.

Since cabs are coming out, could a thin sheet of plywood be screwed on top of the old subfloor to provide a smoother, more level surface if you want to put down something like LVT tile?

Is the subfloor particle board or plywood? That will determine what you can use for flooring to sone extent. I was told porcelain tile needs a plywood subsurface.

LVT tile might be the easiest solution. I hired a contractor to install my floor, but DH had purchased the flooring and read all the specs, so he worked as the contractor's helper and it took them less than a day to install our kitchen, hallway, closet, and mudroom. We also have 3 cats and a 100-pound dog, and after 18 months it looks exactly as it did when it was installed.

There are lots of options as far as what look you want. We chose a neutral stone-type look with lots of variation (Coretec Plus noce travertine) but there are also concrete and wood-look LVT options.

If the substrate is "very soft" it is particle board. It is not repairable. It is often damaged when removing permanent products like glue-down tile. For that reason, most professionals simply take it out with the flooring still attached. It is MUCH faster/easier than removing the tiles AND THEN removing the substrate.

A gouge that big means you will need to remove the fibre board and start over. If the cabinets (all of them) are coming out, then it is easier to rip out EVERYTHING once the cabinets are gone. Either way, the substrate needs to come out and then new stuff put in it's place.

Once the substrate is gone, you can have any floor you like.

If you can get the sub floor good and smooth, either by renting a commercial sander, or putting a thing layer of plywood over it, I would recommend LVP. I ripped up old lino and used a belt sander thru a large area of our cabin and put down EZLay loose lay wood look planks. It worked out very well. I am a 62 yr old female with 2 artificial hips and I did it all myself, so definitely a DIY project. Other than having DH help move the fridge stove and dishwasher and the claw foot bathtub as I did the entire cabin. EZLay and XL Flooring are 2 Canadian sister companies who supply a very good quality LVP. Don't let the term loose lay make you think it won't stay put or will leak spills. It fits so tightly together, water will not seep between the cracks unless you actually have a serious flood that sits for a long time, which will result in damage in most any flooring type other than sheet vinyl. Here is a link. XL Flooring/ EZ Lay flooring I was so happy with the results that a year ago I used XL flooring to redo our TV room at home. Both brands are made the very same and only differ in colours and patterns and a small difference in plank size.

Editing to clarify that the LVP itself wouldn't be damaged in a flood. You could lift it, do repairs and re-lay it.

We just put in Coretec LVT in the kitchen, back entry and powder room. It’s a click lock floating floor. We had to remove old vinyl sheet goods and the underpayment because of the change in flooring heights where the kitchen met the family room. We pulled over 6000 staples by hand...6000! That took WAY longer than actually laying the LVT. We chose LVT because our 90lb lab loves to sprint to the back door and slobber his water.