Yep definitely experienced this. One of my previous companies was twice a year (July 1 and Jan 1) depending on your start day. So if you started Jan 3, you couldn't contribute till July 1.
They also ran other benefits this way and did all of their raises and stock awards based off that too.
My old boss was a temp first back like 24 years ago and started in December. Got hired full time Jan 3 of whatever year. The CFO, who started around the same time as him, always puts together a personalized "This is how much money the company screwed you out of by not back-dating your hire date to Dec 31" statement at the end of every year. 6 months of 401k vesting, a year (compounded) of bonuses, stock awards/options, raises...