As for your argument on checks and balances - yes, generally, it is definitely a very good thing. However, when one side uses their position of chamber majority not to collaborate and compromise, but to throw a wrench into "wheels of democracy" and gridlock the Congress (especially, considering the voting record of the current majority in the Senate and essentially zero breaking ranks history), which might be extremely unproductive and even damaging to the lives of the American people, that IMO does not represent the "checks and balances" that you're talking about.
Senate votes [1] are almost never perfectly partisan (52-48 in current form). They are all over the place. Romney, Fluke others have bounced on some big votes for Republicans, and frankly, we don't always see the 'break ranks votes' because they are usually foregone: Senate Whip won't take it to the floor if he knows there are a handful of stragglers so those 'broken ranks' are not as visible.
[1] https://www.senate.gov/legislative/LIS/roll_call_lists/vote_...
~) Also consider @Steltek's point (comment below): "it's hard for Senators to break ranks if bills are never brought to a vote".
The playing field need to be leveled here so that party leadership doesn't have a stranglehold on what comes to a vote via backroom deals. Legislators need to have skin in the game, with real debate and actual votes to show where they stand.
There's apparently plenty of room on Mitch McConnell's desk. There are already hundreds of bills that passed the House sitting there.
This implication directly contradicts the part about 'unity'.
'One side' having the run of the system will absolutely lead to greater divisions.
Trump is gone, I think most reasonable people will take solace in that. Now that he is gone, having regular checks and balances is a 'good thing'. Having the 'other side' with a narrow, 1 vote majority in the Senate is probably a really reasonable check on power, as Senators often break ranks with the party so there's plenty of room for a 'really good bit of legislation' to get through if the Dems want to push for it.