On whether deleting undermines the system: it does the opposite, and this is worth being direct about.
The deck is a tool, not a record of your intentions. A card you keep failing costs you time every session and teaches you nothing. Multiply that by a handful of cards and it is a meaningful share of your reviews spent on the material with the worst return.
Deleting it is not giving up on knowing the thing. It is declining to use the wrong tool for it. Some things are learned by use, by reading them in context, by doing the task - not by a flashcard.
What I have found after deleting freely for years: nothing bad happens. I have never once missed a card I deleted. If something genuinely matters it comes back, in context, and I add it again in a better form.
A useful periodic habit alongside it: go through your deck occasionally and delete anything you no longer care about, not only the failures. Decks accumulate the interests of previous versions of you, and a smaller deck you review properly beats a large one you dread.
And on the specific handful eating your sessions: fix or delete all of them this week. The change in how the deck feels is immediate and out of proportion to the number of cards involved.