Depends. Tool proficiencies are not just using the tool, it is also knowledge of the art and materials related to the tools.
I definitely wouldn't let 'mending' create new material, so shoes will still wear out eventually.
That's why I specified "adventure-related challenges." Seriously, I've never played in a campaign where shoes wore out. If you play in campaigns where that happens regularly, then obviously tool proficiencies are more useful at your table.
I definitely use the language culture connection in my campaigns. Tools too, but to a lesser extent. Languages are *the* way to add a new body of knowledge to your character. So if you pick up Elvish, you probably know the names and portfolios of the primary elven deities even if you don't have the Religion skill, for instance. I just think "what basic things would almost everyone who grew up speaking this language know?"
I've incorporated many of the downtime activities in Xanathar's Guide to Everything (XGE) into my campaign. This includes training for languages. But to learn a new tool, I use the PHB rule of 250 days, instead of the XGE rule of 10 workweeks minus the character's intelligence modifier.
I'm finding myself waffling on which time requirement to use for training in a new tool proficiency and would like to get perspectives of other DMs.
My original concern was that a tool proficiency represented a significant investment in time working as an apprentice. The PHB's 250 days seems more reasonable than the XGE 10 weeks minus the character's INT modifier. But, with a 250 day requirement, I'm not sure anyone will ever learn another tool. On the other hand, over the course of the campaign, we could easily have a character learning pretty much every tool proficiency if I go with the XGE rules.
I worry XGE devalues tool proficiencies, which in turn makes backgrounds and character creation choices less meaningful. I'm less worried about this with languages. There are many different languages and languages are less mechanically impactful.
There are ways I could tweak it and make home brew rules on having to keep in practice, but I don't want the extra complexity and rules overhead. So, ultimately, I just need to decide on whether to go with PHB or XGE time requirements for training in a new tool.
Which do you use, if either, and why?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.