MS is a process where the immune system attacks the myelin sheath of nerves.
Stem cell therapy will replace the damaged myelin, but does not stop that process. So eventually the MS will return as the demyelination isn't cured.
Whether or not this affects the rate of progression is unknown and likely to stay that way as there's too many charlatans around. (Why does anyone think stem cell therapy isn't a recognised treatment in the UK ?).
In the 30 years I have been following MS research, the closest we've got is a suspicion there is some viral element involved. Possibly in combination with some other environmental and geographic factors like latitude and urbanisation. Things aren't helped by the fact that our understanding of the immune system is just above zero. Throw in how allergic reactions can be triggered and manifest themselves and you're probably up to speed with current research.
Remember that medical science is one of the most staid in the spectrum. So new ideas rarely get aired. I'm still old enough to remember when medical science insisted (insisted I tell you !) that stomach ulcers could not possibly be viral and that anybody who said they were was a gibbering idiot who should be ignored forever. That was right up until stomach ulcers where shown to be viral and if you now doubt that you are a gibbering idiot.
Science is where you mustn't confuse knowledge and intelligence. Medical science especially so.
The only thing that has improved in 30 years (thanks to MRI) is diagnosis. It used to be relapsing/remitting could take decades to be diagnosed. Especially with waiting lists of months. By the time you get seen that pain/twitch/numbness has "gone away" - rinse and repeat. Add to that the previously noted asymmetric sexual distribution and the UKs longstanding shit healthcare for women, and you have a disease that could go undiagnosed for 20, 30, 40 years.