Many responders have already mentioned the cursive handwriting as faster...
In fact, perhaps unlike some cursive scripts I see daily used in Europe/US at least, the seeming purpose of Russian cursive writing is to write a word, or large parts thereof, as one line without picking up the pen from the paper and seeking to a new position to start the next letter of the same word. This "built-in" habit from the school impacts my handwriting in other languages, which some native-speakers (and native-readers) then reported to be curious and not the way they would write the same words and sentences.
I think this also impacts the aspect mentioned above, like interchangeability of "т" and "m" for the same letter - I also have this habit without a second thought, but if I give it a thought, the choice likely relies on what liason from the previously written letter would be simplest to implement without extra momentum to the hand... or maybe adding one if it feels tired from holding one position for a while and needs the slight massage of a more jagged writing :)
My schooling was in late USSR/early Russia, and while there was a strong emphasis (and significant grading impact) during Russian classes regarding legibility of what was written, I don't think there was much stress regarding the choice of variants to write same letters same way consistently.
UPDATE: I asked around, and my wife whose schooling was in early post-USSR years said they were drilled on proper cursive writing with one true font. Variations like the "T" examples above were not tolerated, treated as a mistake - that they twitched and put some garbage in the page and skipped a real letter from a word, thus wrote it incorrectly.
For schoolkids today parents can apparently sign a request on how their children should be taught writing - with cursive scripts and further enhancing that skill, or with block scripts and further move into typing/tapping rather than penning.