If you play the game the way I do (shoot aliens down asap to make sure you prevent them from carrying out their mission), you do need more fighters at higher difficulty levels, if only because the UFOs do more damage (so your fighters spend more time being repaired).
That's not the best way of playing the game. As Meridian said, the best way is to follow them around and assault them when they land. No need to build and maintain fighters and you always get all the elerium.
But to me that's "gaming the game" instead of playing it. We know as players that UFOs land 90% of the time, but if it were you in charge of defending the real earth, would you really wait and hope UFOs land or scramble everything you've got to take them out before they hurt people? Those farms you land on are empty, and I'm not 100% sure it's because farmers are so good at evacuating... Granted, they're empty when the UFO is crashed too..
The tougher question is: After the first few times, would aliens really allow you to tail them to their landing site or would they shoot down your weaponless skyranger? It being impossible for UFOs to engage XCom crafts is an engine limitation that allows this kind of tactic, which is actually the main reason why I consider it gamey.
Another, probably easier, way of "fixing" this would be to give landed UFOs a significant bonus in points scored for the aliens (currently x2) since they are working on whatever it was they wanted to do, which probably involves killing people. That means you wouldn't want them to land.
Regarding Meridian's ways to lose the game, it is possible to address them with mods by:
a) Making selling stuff less profitable / requiring a lot more equipment production, meaning you either need a lot more workshops or you won't be able to manufacture much for selling.
b) Score is tricky, but I think some of it can be tuned. Make civilian casualties cost XCom a lot (people are no longer OK with killing all aliens after they killed all civilians). It also helps with the "protecting humanity" thing. As mentioned above, give a bonus to landed UFOs, that's more points to aliens. And increasing the points generated daily by alien bases (currently 5 per day) so you want to take them out instead of farming their supply ships/the base itself. OpenXCom's bug making the supply ship land only a very short period is actually pretty good against farming too. You can also lower points gained by XCom, in either the geoscape or battlescape.
c) Unless you screw up, losing a base is indeed quite difficult, especially if it is your main one. Even if staffed with rookies and crappy equipment, winning is doable (See Ivandogovich's first base defense with barely equipped rookies). Aliens just trickle in and are really easy to ambush with a well built base. Not much you can do with this one though.
d) Make Cydonia harder!
But really that just makes the player reload their last save and try again..
The game might or might not need fixing, depending on what you want out of it. In general, I think the conditions for losing a game are fine, but too easy to work around. I think the strategic level of the game could benefit from being as challenging as the tactical level (which is really unforgiving and why we love this game).