I suppose if you try hard enough you can justify nearly anything. In this case you're really reaching and it's not at all clear why. Millions of people wear steel-toed shoes and boot at work daily. I personally have a pair that I wear for certain activities and it's entirely unnoticeable that they have steel toes. You're NOT going to win this battle and it's almost certainly going to make you look like a whining, complaining fool.

workgearz.com/best-work-boots-for-ladders

"So I guess I'm pretty much leaning to option number 3. " - terrible idea. It could invalidate an insurance claim, should an accident happen. Are you in a union? Are you the only one who ever climbs ladders? You are new. Give it time. Don't do something foolish.

"having two heavy weights on my feet reduces my agility" <- Agility is not a relevant factor on ladders. How are you climbing them that requires you to be agile?

If you're climbing a ladder in a way that requires any agility and is impeded by some steel caps, that is the safety issue. (By the way, that's the answer you'll get if you ask. And not following the safety rules on purpose is cause for termination)

Is the real reason cost? You don't want to buy the boots? My experiences are usually that.

Safety regulations are written in blood. I worked at a place that required clip-on ties(if you wore one). We had a guy that thought he would wear a nicer tie instead. He was pulled into some equipment when he leaned over it and the tie got caught. Someone stopped the machine before there were injuries, but it goes to show the rules are there for a reason.

You say reduces your agility, but do you perhaps mean it reduces your ability to sense what's under your feet? I could see very rigid shoes making it easier to misjudge what you're standing on, even if you aren't climbing the ladder in a "high agility" way.

Is the policy to specifically wear STEEL-toed shoes? Or safety hard toed shoes? Thus ruling out composite toe?

@BoogaRoo What type of job even allows ties where there are machines that can pull you in?

@DKNguyen Print shop. Customer facing employees could wear ties, but would occasionally go to the back in the production area. In production areas you weren't allowed to wear anything that could snag. I.E. rings, necklaces, non-clipon neckties, etc.. You wouldn't think it was very dangerous, but fast moving rollers, heavy cutting presses, and similar stuff have a lot of leverage and momentum. They can be rather unforgiving.

I personally cannot see steel toes causing a problem climbing a ladder unless you have some underlying condition that would make climbing a ladder in general dangerous. However if you really want to push the issue you could ask for permission to get boots with reinforced toes that are lighter, such as composites or titanium.

I'm going to second Joel Etherton's comment--while I've never had an occasion to wear steel toed boots I do frequently wear hiking boots. They add weight and they considerably decrease your sense of what you're standing on--and that became a non-issue to me in a matter of a few miles. Admittedly, I've never worn them up a ladder.

Wearing my capitalist hat, I speculate that safety regulations may be stipulated by insurance requirements. If a company puts certain rules into place, it can reduce their insurance payments, or increase their coverage (as a business), so the rules are unlikely to be successfully negotiated by the individual workers, but rather are set as a side effect of the company's cost/benefit analysis with respect to insurance options. Collective bargaining may be an approach to make it more costly to the company to incentivise them to change policy - but that may be biting the hand that feeds.

I can totally understand OP. Big, heavy boots just make me feel clumsy. I have a few scars on the back of my legs from crampons to prove it :D

3. is a great way to get fired. You can disagree with the policy all you want, but keep that in mind.