"Going on COBRA" doesn't cost the employer anything if they don't pay for it. All it does is allow the (ex) employee to continue the coverage they had with their employer "IF" the employee wants to pay for it. There's also the provision that the ins co/administrator can tack on up to 2% fee for the privilege. If the ex-employer offers to pay any of the "COBRA" premiums, that's a very nice employer. For employees that had their medical coverage subsidized, it can be a big shock to see just how much their insurance was costing their employer. But nowadays, depending on the situation, a lot of people can get personal/private insurance for cheaper than what their employer was paying. Employers are getting ripped by medical insurers and third party admins these days.
Also, you aren't taxed on the medical benefits portion of your income. Well, not federal income taxes at least; FICA, maybe state.