In principle, giving up the ability to exit deserves payment. In practice the premium is hard to measure, because illiquid assets are valued by appraisal and their reported returns are smoothed, which inflates apparent risk-adjusted performance rather than proving a premium exists.
Some of what looks like an illiquidity premium is actually leverage, sector tilt or small-cap exposure repackaged. Comparing a buyout fund against an equivalently levered small-cap public index removes a large share of the apparent advantage.
There is also a genuine benefit unrelated to return: not being able to sell prevents panic selling. Whether an investor should pay for that discipline through fees, or impose it on themselves for free, is a fair question. See interval-fund and private-equity.
Related: private-equity, interval-fund, liquidity, non-traded-reit, private-credit