When I've discussed the motivation with weight-lifting friends, they bring up that very point. Then I ask them to give an example of something they did with their strength today or in the last month, that I couldn't have done just as easily (I'm average strength).
After long thought they come up contrived examples like, I had to lift my motorbike to change a tire one time, or last year I gave my daughter a piggyback ride for an hour at a parade so she could see better.
FWIW, my motivation for working out is to be better at parkour. It's helped a ton for that, but most people don't do that sort of thing regularly. Being good at shoveling snow is just great.
Probably because you put them on the spot. I can give you several examples off of when additional strength would be useful to me in day-to-day:
* Loading jugs of water onto the water dispenser
* Loading my daughter's stroller into the back of the car (somewhat heavy, very awkward)
* Carrying large/heavy boxes to/from the basement
* Loading heavy items (e.g. stand mixer) into overhead cabinets
* Pulling salal from my flower beds (deep, extensive roots make this a major chore)
* Carrying an Aeron chair up/down the stairs (I've done this several times)
* Moving heavy furniture
* Moving wooden sheet goods (plywood, MDF)
* Hanging my bike overhead for storage
* Holding heavy light fixtures overhead for installation
Less often in day-to-day life. Hitting your limits in the gym means that you don't hit your limits in day-to-day life as easily, so when you need to move a loaded bookshelf, or pick up your spouse and carry them across a threshold, or whatever, it's not a problem.
It's exactly like running so that when you need to run, you can. Want to make it easier to sprint when you need to catch the bus? Sprint more in general. Want to make it easier to climb the 5 floors of stairs to your office? Climb 50 on the weekends.
It's also exactly like anything else you would ever practice for. Need to do complex math at work that you don't understand? You should probably study. Annoyed that you suck at the piano? Spend time practicing at night. Is your broken Italian not satisfactory to you? Spend time speaking Italian.
It's not absurd to spend time and effort improving an area you want to improve. We practice specifically so we can perform when we need to.
(Also, the muscle mass put on when younger has a huge impact on quality of life when older. Strong people hold up better to aging in general. You might not have trouble lifting a 45lb jug of water now. Do you want to have trouble with that when you're 65, 75, 85? Putting on additional muscle early makes it easier to retain a healthy amount of muscle later in life.)
Finally, I'm better at taking all my groceries in with a single trip.
Last week I was moving 150lb barrels of chicken feed.
This month, shoveling snow for myself and multiple elderly neighbors.
Mid-forties, desk job. Weight lifting helped.
The daughter piggyback example is interesting - my initial experience with back pain came when playing with my toddler daughter several years ago. "Threw out my back". Yes, strength helps with everyday tasks.
Guess what? Could lift it up, picked the dropped item, found a couple more that had been lost months ago, and put it back into place.
Additionally, the feeling of accomplishment is awesome, being able to do things you could never do before is just incredible.