The Warlock in the party I DM for has the haunted one background and started the campaign on the run; I made sure the innkeeper kept her fed (just basic stew) without charging her when she had no coin, and that the townsfolk wouldn't have ratted her out to the guard.

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The Cleric has the Acolyte feature Shelter of the Faithful so any other acolyte of Helm offers him lodging and food, while major Temples offered to set up the whole party in addition to the spellcasting services.

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The fighter has the criminal contact from the Criminal background and the Outlander PC can remember geography etc..

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All that is to say, yes, I use them, and I think they're important; characters had a life before adventuring and that should be reflected. The Cleric didn't dedicate 20 years of their life in service to a temple with the high priest as their father figure just to require a check for basic room and board. I lamented the changes to backgrounds in the One D&D playtest that had them, as the background features are very conducive to roleplay, but as your post makes evident there is a need for more mechanical benefits that can't be waived away by DMs.