Is it worth $5000+ extra for rebar (I don't know the upper for wire mesh)?
Not if you are going to install a 4 post lift.
Rebar is not required and is simply insurance against cracking. Its insurance against random cracks, insurance against inadequate saw cut joints, insurance against shallow saw cuts, insurance against general shoddy workmanship.
Cracks are bigger concern for 2 post lifts, which must be bolted down. Bolting is optional with 4 posts, so cracks in the slab don't cause the same level of complications or safety issues.
Instead of spending the extra $5000, you are better to take the day-and-a-half off work and watch your contractor like a hawk. Make sure:
- You have a well-graded, properly compacted base before work starts
- They give you the full 4" you are paying for. (Most contractors don't... they will treat the depth as a minimum or target.)
- The crew isn't slacking off and needs to throw in in extra water or other odd things to get the job done
- The mesh is on proper chairs so it can't sink to the bottom of the slab (where it does you no good)
- A crew returns first thing the next morning to make the saw cuts (no later, no earlier)
- Make sure the saw cut joints are at least 1: deep!!! (If you aren't watching and aren't insisting, this standard [1/4 depth] will not be followed. Its crucial for crack control.)
Discuss the chairs for the mesh ahead of time - if you don't, the contractor won't show with them. You might even just confirm how many you need and buy them yourself to make sure they are on-site:
https://www.homedepot.com/p/Hercules-2-in-Steel-Mesh-Chair-100-Pack-944/315019853
^ Also, don't accept hacked solutions instead of chairs like broken pieces of concrete or bricks. They create weak points in the slab and are not proper substitutes for chairs.