Some engines won't even start or idle properly with one or more collapsed lifters. But dirty oil, sludging etc usually leads to collapsed lifters which is detrimental to engine operation. Hydraulic lifters are nice when everything works. Adding a hydraulic lash mechanism could be an unnecessary complexity which may detract from long term reliability.

Honda may maintain mechanically adjusted 'screw and nut' lash adjustment due to their VTEC engagement philosophy and design. I'd bet that when/if they replace that block, the new V6 will have chain driven cams. The V6 is still using a belt, leftover from its 1996 (I think) debut. The belts were phased out, I think, with the D17 in the 2005 Civic and probably the B20 in the 2001 CR-V. All current Honda 4 cyl models in the US use timing chains. I think there are probably design considerations here beyond plain technological advancement, but I'm not sure what they are. At least with the Honda ones you don't have to remove the cam to adjust a valve if any are off. IIRC Honda is alone in using the 'screw-and-locknut' style tappets, but lots of manufacturers are still using shim-over-bucket ones, including Toyota, Nissan, Ford/Mazda, and more. But when I started looking into it, I found that it's actually pretty common.

I was surprised when I was shopping before I bought my Civic that they still used mechanically adjusted tappets. My 1989 MX-6 had hydraulic lifters you'd think that Honda could make this happen. Don't know if they have advanced to hydraulic (self adjusting) valve lifters yet, or not.

Honda cr v timing belt or chain