Grout wicks water down the grout lines in behind the silicone dam to be trapped. If no silicone is used water just wicks out the bottom of the grout and dries. Before the tear out, the tub caulking acted like a miniature dam to hold moisture at the bottom edge of tile work and promotes mold growth, wicks into green board and will promote rot of the wood. Rubber floor mat and abrasive cleanser caused the tub to wear much quicker.
Water is making its way behind tile to make the substrate expand, further opening grout lines. Probably mold growing in the wall. This is a total tear out and replace situation. Grout repair will not work and my feeling on tub/shower inserts or painting of tubs is comparable to getting expensive seat covers for your car. The tub is not terrible, but I always recommend changing the tub or shower pan. Who wants to have a new remodeled bathroom with an old tub.