Of course that's actually a desirable feature of such institutions. Give them a mission, staff them with technocrats dedicated to the mission, defuse political interference and they'll deliver. The US Supreme Court decided you can't do that (well, in practice, that Democrats can't do that, it will be fine when Republicans do it) but outside the US this is an attractive idea.
However Politicians don't learn, they will always see political advantage from meddling with the independent entity, and then be astonished when such meddling backfires badly.
Take NICE in the UK. The purpose of NICE is to decide how to spend necessarily limited resources to deliver healthcare. How many profoundly deaf 5 year olds being able to hear is worth one grandparent who lives an extra twelve months? If this new drug is $180 to treat one patient while the generic we're using is $5, what sort of benefits does that new drug need to have to justify the price tag? These are the "death panels" Americans were told to be scared of years ago.
But politicians don't care about the general idea of NICE, they care specifically that photogenic Sarah, whose husband happens to work for a news publisher, is dying of a rare illness, and NICE says the $5M drug to cure Sarah's illness isn't "cost effective". Politicians want a photo of them hugging Sarah and promising she'll be OK. They definitely don't want to raise taxes to pay for the drug (higher taxes is unpopular) but they do want that photo (it'd look great on campaign adverts). And hey, the drug maker gives them $50k campaign donation, that's nice. Let's override NICE and divert $5M to get Sarah the drug. Oops, Sarah died anyway, oh well, news moves on.
Years ago the Tories introduced a "cancer fund" where for no discernible reason if you had specifically cancer, there was a separate pool of extra money so that they could be shown to be such compassionate people, who really want what's best for everybody. Well, not everybody of course, just people with cancer for some reason. Of course then photogenic people have something that's not cancer and you look really callous because you rejected them. Wow, it'd sure be easier on politicians if these funding decisions were made by some technocrats instead... oh right.