Put-call parity [1] makes option markets work. It lets anyone to manufacture a put from a call and a short, or a call from a put and a long. This ability to spin up options on demand is critical to options market making. (Source: former options market maker.)
Take away shorting and you vastly increase the risk of correcting option mispricing. Given how fundamental options are to other instruments, e.g. convertible debt, this would directly decrease funding options (and increase funding costs) to companies.
Saying that, for most amateurs I'd recommend selling puts than shorting since shorting has unlimited downside risk.
Sometimes shorting against the box makes sense if you have the asset in another account and can't sell it there. You could short it in your primary account and then move the shares over which make take a few days locking in a sell price. When the shares arrive in your primary account it covers the short position.
It's not a clear-cut situation - in times of turmoil, when many traders are considering a short, the price of options will rise. If the situation then calms down and the price of the underlying decreases steadily, the drop in the option price due to lower volatility will offset a lot of the potential gain.
When expressing a trade using options one has a lot more parameters to deal with in order to formulate the risk-reward properly. I'd say it's exactly the sort of thing most amateurs shouldn't be doing.
My biggest caution against shorting a stock VS a put is the potential loss. At least with a put your loss is capped.
I'm not a derivatives trader but have explored investing in options when I was at a fund, and that was my experience looking at options for hard to borrow stocks. For market makers out there -- is that a fair assessment?