The collet chuck won't come loose and become a flying bullet. If the money isn't there, don't be concerned about it, I used a drill chuck to hold mandrels for years, the collet chuck for a wood lathe is not that old, maybe 20, I don't know, but I didn't get mine until about 7 or 8 years ago. With a drill chuck you have to use a drilled blank and a blind mandrel, it work, just remember, no draw bar your drill chuck can come loose, so always use your tailstock.
But when funds become available, I would get a collet chuck.
Marvin