Not exactly like them, but Tiny Combat Arena recaptures some of the joy of flying these polygon-based, simplified flight model flightsims. It's still in alpha (so only one playable aircraft -- a Harrier -- and only one demo campaign), but fast approaching 1.0, and I recommend it.
If you want to fly a "modern" jet without needing to read a manual or learn very complex radar systems, this is the game for you.
Tiny Combat Arena's sole developer Why485 is very active on twitter & previously on their blog.
Both profiles are well worth a scroll through if you have any interest in sim-lite games. Really like the breakdowns on old school simlite games and what really made them fun (since it wasn't strictly a matter of realism = better).
Agreed it's definitely not a matter of realism = better! DCS looks gorgeous and very realistic, and I know it's simply not for me, because I don't want to actually work as a combat pilot.
MicroProse's F-19 is the flightsim I played and enjoyed the most, and it wasn't realistic.
DCS has some very advanced sims but some of the cheaper modules (planes) are intentionally less realistic/labor intensive.
If you download DCS World directly from the site instead of getting it through steam, you can get a 2 week trial of each module every 6 months.
Flaming Cliffs 3 is the name of the less realistic module. It comes with several planes or you can buy them individually. As I said before, you can try them all for free for 2 weeks each and it resets every 6 months.
I always loved the GraphSim F/A-18 Hornet sims. They were simple but still decently realistic. I still have mine on an old PowerMac tower! I should play that again.
Actually they have an iOS version, which isn't bad, except the lack of joystick support.
Falcon 3 and 4 are major milestones in "serious" flightsims, and I toyed with both of them (3 more than 4), but I cannot say I completed a single mission with either.
MicroProse F-19 hit that awesome spot of some realism (laughable today, but it wasn't meant to be an arcade game back then), with a really easy flight model and cool missions and scenarios you could really complete. And besides knowing the keyboard mappings, you really didn't need a manual. It was thrilling to play mission after mission, getting all those medals, and having your character be promoted in rank. I spent a lot of time with that game -- probably flew as many missions as an actual combat pilot!
The only other flightsim I found almost as engrossing was Gunship 2000, with its "dynamic" campaign system, but it was way more difficult.
I find Tiny Combat Arena captures some of this thrilling but simple gameplay, but it currently lacks content (more campaigns, more maps, more things to do).
If you want to fly a "modern" jet without needing to read a manual or learn very complex radar systems, this is the game for you.
https://www.microprose.com/games/tiny-combat-arena/