Advice on re-grouting this shower
I would venture to guess that originally the shower had a properly waterproofed substrate; the common inspector's test requires plugging the drain and filling the pan with water for a period, checking for water level change.

There may be concern now, because cracked and failing grout can be a sign of movement (there are, however, other possible causes of this). I grouted my shower 23 years ago and the grout looks practically the same as the day it was done, so something is up.

If you have confidence, and you should have some due to the fact that you have not noticed any leaks, you could carefully scrape/grind out the remaining grout from the entire area and regrout. I have had some success using a combination of utility knife (get extra blades) and grout saw, and you don't have to remove all the old grout but try to get a channel at least 3/16" deep.

However, grout is porous and will not help over the long term if the pan is compromised. I feel that you should do everything possible to ensure there are no leaks. Slow seeping pan leaks can be difficult to detect, until the floor drops out from under you or a ceiling above falls in your chiles relleno. Even if it means having to open up a wall or ceiling for inspection hole(s), it will be cheaper to patch drywall than to repair the damage of a long-term pan leak.