The line doesn't need to move quicker, and Ukraine moving slowly and shoring up every meter they take is going to work out better long term. They aren't on a march to invade their lost territory, they are on a march to the Azov sea to cut Russia's only remaining land access to Crimea.

They are building a wall of men and weapons and once that reaches Azov they only have to defend it - and Ukraine are very good at defence.

Then the only way Russia has to get anything to Crimea is the Kerch bridge which is almost inevitably going to be destroyed.

Depends how deep the lines are. They have breached the first line at some points. However as per ukrainians, after the first line is the second line and so on. Russia knows how to make deep defences and anywhere, where they lose one line, they will adjust and start added more lines to the rear to compensate for the lost line. First line lost, second line is now first line, third line is second and so on and add the new Nth line, since the old Nth is now Nth-1 line.

It will be a slow slug and battering ram fest, unless Russian army morale breaks/ supplies exhaust and they run.