Senate served two purposes: (1) A recruitment tool for getting more users and streams involved. (2) Serving as a check on the ambitions of, frankly, IncognitoGuy and his Memechat Empire.
The effectiveness of (1) isn’t entirely clear. Several are arguing that Senate makes things needlessly complex here and actively drives people away. I don’t know how to measure either theory, but it seems hard to imagine someone getting excited about this stream because of the Senate in particular, a relatively obscure institution that even regulars don’t fully grasp.
Re: (2), in the bad, old days whenever IG’s bad, old Conservative Party won an election, many of the stream’s most active users would be passed over and iced out of Congress, in favor of Memechat Empire randos who only ever showed up to vote precisely as IG told them to, if at all. So, Senate was for a time an institution that resisted IG’s corrupting of Congress. As OP said above, for several reasons (IG’s ban, reform of Congress seat appointments), that dynamic no longer exists, calling the need for a Senate into question.