Often I find myself with 1 leader, 2 or 3 engineers, 2 or 3 navigators and a fistful of assorted others after a mission. At the beginning, leaders have, for example, 25 techs of which 5 are useful. One pull at 20% isn't great and early on leaders aren't easy to come by, so if you interrogate a soldier or two first, then the navigators, then engineers, you might get those odds up to 25 or 30%. If you are swimming in Leaders, sure, but an early hit on one of the important techs can improve survivability in the mid game substantially, so I do my best to maximize the chance on early pulls of the wheel.
As to a fix, well, it's hard to say. The "substantial breadth" is a big draw for XCom Files, the issue is just that it is a mile wide but inch deep at some points, often when you've stalled and are waiting for that one mission type you need to advance to spawn. You could add options to make it easier to get those techs, or alien techs in general, but that'd just exacerbate the wait for specific spawns near the endgame. Long term, do you have a goal for how research should work in the end game? Is it expected that the player will fully research every option? One path some games take is to provide research chains that while not mutually exclusive, require more resources than the player has to fully explore by the end game, sort of like a softer version of the codex from Xpiratez. So instead plasma being the default endgame weapon, maybe have terawatt laser, warp cannon, and monofilament flechette, but each requires a data core that is a one off from a very slow to reoccur mission and the data core has to be "cracked" providing only one of the technologies.