Problem is, DI isn't really a workers comp replacement. If you are out for 2 weeks, the DI coverage won't even kick in. If you have large medical bills, health insurance may exclude coverage since workers comp should apply.
Other issues as well.
Most DI is non-occ, not 24 hour. Try finding 24 hour coverage on blue collar with benefits to age 65 (or whatever the WC cutoff age is for benefits).
The medical is less of an issue, depending on the size of the group.
You also have the accidental death issue. Most AD&D is also non-occ. You can find 24 hour AD&D on some group plans.
Replacing WC liability (life, disability, medical) is not as easy as it sounds when doing a hodge-podge, cobbled group of policies. There are gaps that cannot be covered by a non-WC policy.