Most businesses would very much prefer NOT to have to deal with employee health plans. Forgetting the cost to them - it's a massive annoying overhead and nightmare to manage.
Big businesses would prefer it. They already have the huge HR departments to manage it, and it serves as price obfuscation so the worker cannot accurately compare alternative employers’ offerings.
It also works against small businesses that cannot afford to offer health insurance, because the small businesses’ employees cannot purchase health insurance with pre tax money, while the big businesses can compensate people with pretax health insurance that they subsidize.
It’s also a huge disincentive to switching jobs: I’ve known people who took or stayed at jobs they didn’t love just for the benefits who would have preferred to be independent or at small companies but had families, various conditions which didn’t prevent working normally but would have made individual insurance prohibitive. The ACA helped, but not enough and not in every state — especially because large group plans can mean less pushback on every charge.
That may be true, but it’s not annoying enough for them to prioritize doing anything about it. We’d see them forming coalitions to counter the insurance lobby were it otherwise.
Also I’m skeptical that they don’t actually want it, per the sibling commenter’s remarks. I think bigger businesses are all too happy to have another lever of informational asymmetry to pull to manage their actual biggest cost: salary.
