bluejekyll is right that long-term you move the tax burden from income tax to capital gains tax which has a benefit (in my opinion not benefit enough).
As a shareholder of the company you can't sell whenever you want, e.g. there might be restrictions that if you find a buyer all other shareholder have equal right to sell to that buyer. You can't assess the value because private companies rarely assess themselves (tax reasons, strategic reasons) and who you're selling to can also be limited, e.g. by requiring full board approval.
If the company is in trouble at some point then investors and shareholder watch each other (in the negative sense) and it's get political who can sell and how much. In worst case you have to deal with power play in the board, an in-transparent situation where you might not even know all the players.
As you can see the risk increases. Only worth it if you want to their get more control (board seat or get your voice heard) or if you want to keep stock rather than stock options in case you ever get fired or similar event (because you'd loose the options usually).