Not only no better, but actually worse - if you add a word problem around the problem that doesn't fundamentally add anything or make the problem easier to understand [0] all you've added is another layer of text to parse through.
[0] Sometimes it can be helpful. Adding a relevant layer of physicality to help reason about the problem can be nice, especially in calculus.
I think you've hit the nail on the head here. I had tremendous difficulty with Calculus in High School. Everything was introduced via mathematical derivation an proof. I'd gone over halfway through the year with Cs and Ds and, even though it was almost 30 years ago, I remember the moment it clicked. I was sitting the library working on some problem about pools draining and "OMG, it's just about how fast things are changing" popped into my head. That made derivatives, area under a curve, and all of those things make sense to me.
Ironically, I ended up being the only person in my class to get a 5 on the AP test and then ended up as a EE major, which was very calculus heavy.
To try and inspire people, though, maybe word problems could be written to be more relevant
Oh, I’m taking a test it over polynomial expressions —- I already know how I’m going to solve whatever word problems I run across.
Until Calculus/Physics though, I don't think there's much added benefit - except maybe an occasional "here's how algebra helps while grocery shopping".
Seems reasonable that as you introduce new concepts having a physical equivalent would make it easier.
This helped me to “trust” it in more advanced contexts where geometric intuition becomes exceedingly difficult.