It’s not quite that simple.
The Senate operates on a legislative clock, and certain Senate actions require a certain amount of time to be before the body before the next action can be taken.
Senate actions can be proposed under unanimous consent, whereby approval of a bill, resolution or proclamation simply occurs as long as no one objects. You may remember a bill about permanent daylight saving time passing the Senate via unanimous consent previously this year.
Lots of stuff passes the Senate by unanimous consent - post office naming, resolutions honoring some local notable, dubbing the third Thursday in April National Chocolate Chip Cookie day, the passing of former Senators and the like. Hundreds, maybe thousands, of these get passed every legislative session.
But once something is denied unanimous consent, it requires some legislative maneuvering - “debates” are given a minimum amount of time along with cloture votes and voting periods on the legislation itself. All of this will take time on the legislative clock, as will things like executive and judicial branch appointments. And there is a limited amount of time on that clock during the session, and if you try to extend it by doing things like holding members over scheduled holidays, you’re likely to find fewer things passing by unanimous consent, thus taking more time on the legislative clock. For example, a normally noncontroversial ambassador to, say, Mali, might have their appointment held up because a Senator is ticked off at leadership for not being able to get home for his daughter’s wedding.
So Schumer has a limited amount of time to schedule things to get through the Senate, and a lot of it has to go to various “must-pass” things like the various appropriations bills. Schumer can’t just bring up stuff to try when he knows its going to fail, as long as he needs to actually get stuff done, because the time taken on the failure bill might eat into the time that could be taken to pass another priority.
So simply saying to Schumer “you never try” is a bit unfair, given that he’s actually trying to get a larger legislative agenda passed that’s bigger than a single issue. Schumer’s not above forcing the Republican Senators into an unpopular vote or two, but he has a lot of fish to fry.
A cynic might note that McConnell has an advantage, given that he usually doesn’t care much about actually passing legislation and can clutter up the legislative calendar with various votes on wedge issues. As is usually the case, it it easier to destroy than to create.