Even putting performance penalties aside, setting minfree to 0 (or too low) could cause unfixable filesystem.
Once the filesystem becomes full by non-root user writes and the write is NOT finished (it may be quire rare that the last file to be written occupies exactly same free sectors/clustors), it causes crash of the process that writes it as already explained by others.
But what if the quite rare state happenes, and any of the users noticed something needed to be deleted?
The deletions are NOT always simple "overwrites" of existing metadata, even if softupdates nor journaling (regardless via UFS or via GEOM) are activated.
And if any additional sector(s) is/are required, there's nothing to do, except adding new drive / partition that can create larger filesystem and copy everything to it, then alter to it.
If there are some spare space that root alone can write into, users can request root to delete some specified files and root can forcibly delete them.
And more likely-to-happen situation is, if some crash (related or unrelated with the "disk full") happenes and the filesystem is left "dirty" flag on, fsck (as root) should be invoked on following reboots. But if there's no sufficient free space, fsck cannot write anything that are needed to fix the filesystem (you'll remember, this usually happen with unfinished writes!), thus, unfixable.
Performance reduction is important, but this is fatal.