Top tier SAM carriers

A few years ago I heard a rumour that because the BMP-2M has fire on the move missiles then so should the ADATS (because they both have beam riding missiles). I was wondering if any other SAM’s have this ability. Similarly I was also wondering if most of them had any stabilisation systems (considering the Tunguska and Pantsir are both stabilised).
Would this be a good change or just a bad idea?