Tools do need to be stored in context.
I was stopped at the age of 20 and the officer searched my car. it was at a time when there was some debate over it and there had been a recent SC decision on it.
Regardless, I had a 16" flat tip screwdriver between the seat and tunnel for self defense there. And it was because other drivers have been aggressive about me being on the road. The officer explained the stop was because I was driving a similar car - red 66 Mustang convertible with white top - who's owner was a known bad boy and getting official attention whenever possible.
I was asked to put the screwdriver in the trunk. I did and we went our separate ways. Two things held out for me, 1) the cars had hubcaps then and I was having trouble with them, I explained (because they were falling off at the cornering speeds I was getting up to,) and 2) I had my tool box in the trunk.
For all the implements of destruction you might want to carry expediently, you need a plausible reason. I'm not carrying pink workout weights or tacticool water bottles around all day. Most of us won't. But we can carry other items for their specific purpose, knowing they also have an alternate ability.
The OP started this with "improvised," not "tacticool," of which there are hundreds of items for the 5.11 dress up set who need to have Brands blazoned all over their gear for all and sundry to see. Point being not all of us are range warriors strutting around at work like turkeys on display. Some of us aren't playing those games - for whatever reason we prefer the grey man game and not telegraphing our (lack of) skills to the world. So we choose ordinary, commodity items - that can be extremely disabling or even lethal under the correct use. Things that are not considered lethal by design or intent.
Like, the jack handle two steps behind the counter at work. Or the 1/2" drive breaker bar out in the tool aisle. Carb cleaner spray in the chemical aisle. A jug of antifreeze two steps to one side. Metal cans of fuel additive which can be used as blunt weapons. Ink pens in my pocket.
We are surrounded by weapons right where we work, the point of the thread (I thought) was to recognize them for their alternate use in extremis. We wouldn't have any issue coming up with half a dozen if the scenario was a bar - bottles, mugs, stools, pool cues, etc all leap to mind.
What do you have within arms reach that you can use? Even a librarian has at hand materials. One tightly rolled up magazine and they can go full tilt Jason Bourne on some poor patron two days late paying their fines.
Pink weights? Ok, valid if and only if you're at your favorite gym. Nobody really plans to go grocery shopping with one in their pocket, I hope.
What else do you have within eyesight?