Ukraine's own releases state they are moving at a speed of 1-3 km a day, invasions tend to slow down as they age, and we are not near seriously threatening the train route you are referring to, which is Lgov.
There is one big stuff: the longer you will advance, the longer should be supply lines for troops.
Russia for example in Luhansk and Donetsk oblastj had used flowcharts that when some area is taken, immediately trenches etc are digged ( therefore shovels tales ) and minefields installed ( ofc with maps ) and after this push forward.
Slow advance also is very important for security reasons : civies in attacked areas, if they does knows some days in row that there might be ....
Then majority of pro ukr oriented or ppl who does fear from Russia....will evacuate and relocate.
Then in villages mainly will remain ppl who are pro Kremlin oriented or simply doesn't care......
Then after taking village are considerably lesser risks to hold village and better chance to do successful " referendums " after physical control is established.
For example village with 50 inhabitants.
After week of coming up liberation in village are just 10 inhabitants , from these maybe 5 are pro russian and 5 just doesn't doesn't care... so you easily might sent agitator with application forms for citizenship and ofc also to do " referendum " with success and easily to install local " starosta " ....
If vodka and cigs delivered, from these 10 ...more than 5 will be happy and accept new rules..
Low expenses to maintain control if compare with situation if village with all 50 inhabitants had been taken in few hours....