At vesting time you are taxed (immediately) at ordinary income rates on the fair market value the day that it vests, and that's what the cost basis is set to. If you sell on that day, your capital gains from the sale will be (near) $0.
The only reason to wait for LTCG on RSUs is if you decided to hold it for some non-zero amount of time after vesting and then the stock price shot up. But then you're also taking on the risk that the stock price will drop again before the year has passed, and end up with less post-tax money than if you'd sold at short-term tax rates.
Some companies might make you hold for a few months until the next earnings report and trading window. After that it depends on your tolerance for risk and your attitude about the IRS.
Earnings reports happen once a quarter between the company and the public. A couple of business days after that, employees (without material nonpublic info) may trade company shares for the next month or so. Maybe you can't sell April shares until mid-July, and then you have to decide whether to wait until next July to minimize tax on gain.
Sometimes you can elect to sell every released share in a quarter, or file a 10b5-1 plan with a schedule, but you have to do that during a trading window.
Most (all?) public tech companies have policies that prohibit employees from trading the company's stock outside designated windows following a quarterly earnings release.
The only reason to wait for LTCG on RSUs is if you decided to hold it for some non-zero amount of time after vesting and then the stock price shot up. But then you're also taking on the risk that the stock price will drop again before the year has passed, and end up with less post-tax money than if you'd sold at short-term tax rates.