It makes the game a better game because the 20s and 1s are some of the most exciting and memorable moments. And many of us let them be automatic successes or failures not because we don't know the rules, but because we genuinely enjoy playing that way.
Saving throws automatically succeeding or failing makes the game better, because otherwise there are times the saving throw can't possibly succeed or fail. Automatic successes serve bounded accuracy.
Ability checks are more problematic, but DMs simply shouldn't be calling for checks on impossible (or impossible to fail) checks. I'm not sure if published adventures actually use DC 30 checks (I've never seen or used one), but yes, under this system you should not gate things you actually want to be impossible behind DC 30 checks, you should just make them impossible. If they are possible for someone through extraordinary skill, they should be possible for anyone through even more extraordinary luck. Yes 5% is not really all that extraordinary, but sometimes the reality simulator should give way to being a fun game.