I REALLY feel like people are overstating JLIs power. While I havent tried cav rifles, I have used AEs extensively, and they simply destroy JLI. Basically, AEs, cav rifles, and rangers should easily beat jli squads on a 1 for 1 basis. Combat wise, JLI are grens with better RA, a g43 sniper instead of an mg42, and an ambush bonus (which grens can also get with the right doctrine).
They're not equivalent at all.
Against an LMG42 Grenadier squad in green cover, you can take another piece of green cover and coverfight it, with the result being down to numbers and weapon ranges as usual. You've also got the option of rushing in with a CQC unit, in which case the Grenadier has to retreat.
Neither option works against JLI. They've got such extreme bonuses against squads in green cover that your only option to fight them is to close in, and then they've got Sprint to escape that.
Your only options are heavy investment in doctrinal CQC and light vehicles.
It feels a lot like playing against a Sniper. JLI are counterable, but they're not fun in the slightest. I usually want to just hit /l there and then rather than play against them.