These offers usually don't let you sell 100% of your shares. I was at a company that did two offers before the IPO and the most you could sell was 20%.
There's a bit of game theory at stake, as to what you tender. You want to cash out a certain amount to diversify... but if too many people say yes, then your stake is whittled down to due to oversubscribed interest on the selling side.
You get one shot to put in for your % number, and it will either be that, or proportionately lower depending on every other eligible employee's interest in selling.
I recall the max was throttled at 50% vested shares, or something like that anyway for Uber. And you had to have a minimum number of shares vested to participate (low tens of thousands overall as I recall?)
Anyhow, I put in for the maximum both times which worked out because that % got whittled down since the tender offer was filled on both occasions (as I recall).
(P.S. Not that it matters for the story, but $40/share in July 2018 and just under $33/share in January 2018 ended up working out great compared to what happened subsequently.)
However, on the other side... you have long standing employees of the company! So they are by definition insiders. And you'd have to think that some subset of employees actually would have info about the company that buyers in the tender offer process wouldn't have, particularly execs or in finance or maybe some key component of technology that the company's ultimate success hinges on. (Else, you wouldn't see public company restrictions on employees trading shares.)
I believe the general thinking around tender offers is they're often done on some level of discount on what an "open market" offer could be, at that point in time. In part, that's because private companies like to control their cap table. And so you're right that this dramatically reduces the competition in the bidding process as basically it's large funds/firms. Of which there are way fewer than, say, retail investors and smaller funds who would be willing to buy fractions of a few dozen employees' stakes.
Nevertheless, many people taking tender offers are not necessarily doing so out of desperation for liquidity per se. It's an opportunistic way to get some value out of your having worked to build a company, besides salary.