Floor outlets for supply air are installed with us. However, we also heat through them.
No dirt, if children sometimes throw something in, just lift the grate and take it out.
Draft. Now in summer, when only fresh air comes in, I have to stand barefoot on it to notice anything. In winter at full load (heating function) there is a draft. That shouldn't be the case for you.
I find floor outlets less disturbing than wall or ceiling ones. Cleaning is possible without a ladder, although the exhaust air filters need to be cleaned more frequently and they are at the top.