Your mmr is more sensitive to change during placement matches compared to regular ranked matches, and your rank after placements is based on whatever your final mmr is. Your mmr from previous season, while soft reset, is by far the biggest factor, so one can usually guess where they'll end up (~1 tier below where they ended in many cases, give or take a couple divisions based on placement matches and whether their mmr and rank were comparable).
They're still important matches though. Someone who ended the season with a bronze 5 mmr will probably be placed bronze 5 even if they go 10-0 in placements. However, going 10-0 in placements would probably result in them getting 20+ LP for wins since they've done a lot of work in fixing their mmr, while if they were just plopped directly into bronze 5 without doing placements then they might be only getting 10 lp for wins.
Up until master, MMR is the only thing that really matters, LP and rank are just sortof cosmetic overlays to your mmr. If you get a good mmr, a good rank will soon follow, but if you good a good rank without a good mmr, you'll have a really hard time even maintaining your rank and probably trend downwards until they're in agreement.