It’s sloppy and loads of fitters do it that way as it’s quicker. But it leads to heel & toe wear. It’s probably not grippers correctly and that’s why it’s loose as well.
Also you need a clean sub floor if using a water mix smoothing compound. No contamination of old adhesive , paint etc. Also if older then 1980 you will probably need a liquid Dpm.
Have a look on the all in all trim website for cheaper trims. Are all the doorways short of the doorway like the picture ? You will need to notch the trim around the door moulding.