Veneer would not be a good idea for a variety of reasons.......
It is, by design, very thin. Even light use will quickly slice through it.
Since it is glued on, the chances of the glue releasing are extremely high since most cutting boards washed after use.
The reason no actual "finish" is used on cutting boards is because any kind of hard film finish will be sliced off and then enter whatever food is being prepared. Among other things, mineral oil blocks the pores from contamination allowing it to be cleaned.
The tools don't make the craftsman......a true statement often overused by individuals who haven't a clue about quality tools or true craftsmanship.