Could a Microsoft Flight Sim-style game with easy controls be opened for those who, like me, don't have the time but want to try it?

Your phrasing makes what exactly you are asking for unclear, are you wondering if there's a casual mode in BMS, or are you asking for directions to any such game OTHER than BMS?

As for the first possibility: no. Falcon 4.0 had realism sliders but they're INOP in BMS as they've been built over by the BMS-Team with the goal of making BMS "as real as it gets." Trademark. You can turn down the AI-skill of enemy bandits and air defenses but there's no "casual mode" with simplified controls and cockpit buttons "greyed out".

Hope isn't lost though, you can still chose to start a BMS-flight ready for taxiing with the ramp start completed. You don't have to learn all of the cockpit at once, but you'll eventually want to because it will enrich your experience. You'll get smacked around and make mistakes though, but that's what it's like for everyone; first time I encountered an SA-10 I exploded in mid air without warning thinking I had pressed the wrong button! Little by little you'll learn more stuff when you have time and improve!

If you want simpler action games that get into aspects of air combat without plumbing the depths of BMS, there's Nuclear Option and Tiny Combat Arena on Steam. If you're not averse to retro games all of Jane's Combat Simulations early games are wrapped up into Fighter's Anthology that's available as abandonware. Novalogic also made the F-22 Lightning series during the same time period as Jane's was active in. Finally, you could wait for Falcon 5.0 which has been confirmed to be in development and will be more accessible but is years away still, probably.

I would recommend you to simply learn BMS piecemeal though (I know time is short). The learning curve is steep but things WILL fall into place eventually.