We use straps, load rated ones, for lifting all the time. But the ratchet is the thing that worries me about lifting. It just adds another thing to need regular inspection before use, only what would you look for (worn pawls, missing or sticky spring...). And would the winding of the strap tend to make it wear more quickly, or does the relatively tight wrap radius make the strap weaker (like a knot factor)?
That said, #3 son uses what is essentially a ratchet strap for slack line practice. Not sure how high he's gone (I think less than head high) with it.