RSUs are a decent way of aligning company success with employee success. But there's plenty of pitfalls with RSUs too.
1) From an investment risk perspective, your personal livelihood is already significantly tied to the company because you rely on the company for a salary. Holding a significant chunk (relative to your total investments) of stock in your company as well adds to that risk.
2) Unless you're a C-suite exec, your actions will likely have no direct impact on the stock price. And obviously, insider trading is illegal. That means holding your own company's stock has no fundamental advantage over holding stock of a company you don't work for. If that's the case, you're better off picking stocks based on actual performance and eliminate the personal bias.
3) You can sell your RSUs once they vest in order to diversify, but you have to wait a year after vesting or short term gains tax will apply to any gains post-vesting. So, it might be advantageous to wait a year if you don't plan to sell immediately upon vesting. Also, with some companies, a portion of your shares will be surrendered back to the company to cover income tax on the shares.
4) From a tax filing perspective, RSUs and ESPPs can be a PITA. In my experience, tax software and general tax filing services often don't know how to correctly record the cost basis, which means you end up getting taxed twice if you don't know what you're doing.
5) When cash is tight, companies might lean more heavily on RSU-based compensation if they can't afford raises or cash bonuses. You need to make sure your company is giving you what you need.
6) The golden handcuff effect. You want to leave for a better job, but you've got a nice chunk of RSUs that haven't vested yet and could be worth quite a bit in just a couple more years. Is that new job worth the opportunity cost of giving up those shares? For companies that award RSUs as part of yearly performance reviews, you're pretty much always going to have some RSUs that are 3 years out from vesting. It's just difficult weighing the potential value of RSUs vs a new job's salary/benefits and whatever reasons you wanted to jump ship in the first place. It's very personal math and ultimately you have to determine an answer for yourself.