Legally (and theoretically), one sided indemnification clauses are bad, and your lawyer is committing malpractice if they do not recommend removal or modification.
But practically, you have little say if you want to take up the yoke of employment for The Man. Plus, as an employee there are many unwanted responsibilities, not addressed in your contract, which The Man can impose for which your only recourse is quitting. This is one of the biggest risks of being an employee. But the risk of a hospital getting lawyers to sue you under an indemnification clause is infinitely low. There is no benefit to a large system wasting time and money on a lawsuit that will put you into bankruptcy. (BTW, have you ever requested a copy and actually read ALL of your insurance policies? Do you even know what your car, homeowner's, disability, and malpractice policies exclude?)
If the balance of power were closer to equal, for example, negotiating a contract to work for a psychiatrist's private practice, then the indemnification clause absolutely must go. This is because the likelihood of you getting sued by a business owner over some random conflict is much, much higher than being sued by a business. Humans are emotional, large institutions are not.
It's ironic that psychiatrists, despite some training in statistics and psychology, continue to overestimate mostly irrelevant risks while underestimating larger financial risks such as divorce. Insurance companies are happy to insure OB-GYNs, teen drivers, and bars, but I haven't heard of any insuring against divorce. I wonder why.
So if the NP or nurse makes a mistake, I am responsible (say they give a patient that the chart says they are allergic to). It feels like this is a lot of liability.
The hospital will be sued if an NP or nurse makes a mistake because the hospital is the employer. You will also be sued because... doctor. The hospital has its own insurance, with a much larger limit than your med mal limits. Again, the hospital and its insurance company has no interest or benefit in suing you and waiting for a payout, if any, from your bankruptcy.