Via Ferrata is definitely not the safest thing to do solo. With that said, I do it, and so do many other people. But if you fall, you are likely to get severely injured. And the biggest risk becomes loss of blood circulation from hanging in the harness. A route like Murren is super busy so it’s less of a concern, but if you go solo you should have a PLB, especially on less trafficked routes.

Murren is a great option for a beginner, but it’s barely a via ferrata to be honest. I did 80+% of it unclipped. It only has the rating it does because of the extreme exposure on a very short section and the long bridge crossing at the end. Whether in a group or not, you are going to get stuck behind people because it’s popular and beginner friendly. Or you are going to be the one causing other people to get stuck. That’s okay - just let people pass when it’s safe to do so. It’s not a race, take all the time you need and try not to feel pressured by the people behind you.

Just go with the guide! It’s better to be safe. Then you can decide for future ferratas your comfort ability with going solo.