If Ukraine uses ballistic missiles to target Russian infrastructural facilities, then the latter in all probability will retaliate with nuclear strikes. And that will trigger a new world war, where no one is going to win.
While I do agree that Ukraine massively attacking infrastructure on Russian soil wouldn't help ending this war and it would probably make Russia retaliate via tactical nukes if they feel very threatened by it, I am not so sure that it would automatically cause ww3 and nuclear holocaust like everyone is assuming. Its easy to think that US or UK would automatically nuke Russia who would then nuke them, but when you think about it a little bit more, are you sure that they would be willing to sacrifice their almost entire population for the sake of another country? I honestly don't think so.
We are talking about nuclear holocaust. In such scenario, even a 1% chance should not be taken lightly. IMO, here are the possibilities:
1. NATO providing Ukraine with ballistic missiles (50% chance in the next 6 months) - Russian infra gets hit, thousands of civilian deaths.
2. In case scenario #1 realizes, Russia will retaliate (~100% chance). They may use tactical nukes, or they may go for other options. In case they use tactical nukes, then even their strongest allies (Iran, China.etc) may turn against them. So in case Russia retaliate after scenario #1, I would assume there is a 10% chance that they will use tactical nukes. 90% chance is that they will go for other options (thermobaric bombs, white phosphorus munitions.etc).
3. In case scenario #2a (nuclear) get realized, I would assume that there is a ~25% chance that NATO would nuke Russia.
So as per my wild calculations, the chances are 50% x 80% x 10% x 25% = 1.25% (significant enough to be taken seriously)