Apple did make a device that works with all carriers, it's your carrier that has their tower not configured or optimized properly.
This is why standards exist; Apple's phones comply with standards, if Verizon doesn't want to configure their system properly, it's not Apple's issue, sorry.
Apple can ask Verizon to fix the issue; Verizon is quite likely to not worry about it because you're paying your phone bill and it would cost them money to send a tech to the tower.
Note that when people had similar issues when the iPhone 12 was released, in every case I know of it was fixed by the carrier finally fixing the issues at the local cell tower or via a carrier settings update; it was not fixed by an iOS update.
If you ultimately can't live with it, you have 14 days from the date of purchase to return your iPhone for a full refund and purchase something else. (Note there are various threads on other message forums detailing similar issues with newish Android models for the same reasons.)
Using your own logic, if there are four bands new to the iPhone 13, since the BSC will assign frequency bands based on congestion, as the least congested bands odds are all new iPhone 13s will get assigned to those bands as the others will be clogged with every other type of phone the BSC is dealing with.
Ultimately, as the customer, you (at least theoretically) have greater import than Apple does since you're the one that can switch to T-Mobile or AT&T if you like.
I don't expect you to call in complaining about a frequency band, as there's no way for ordinary users to even know which frequency your phone is using, but rather you call and complain about poor signal and service. Eventually your carrier will see a pattern - "Hey, only iPhone 13 users connected to tower 4317 are complaining of low signal." Then it's a matter of if they think it's worth sending a tech out and when; it could be the next time any maintenance is due at the tower over the next year or tomorrow, if it's a local CEO who's threatened to switch his 1500 corporate cell phones to another carrier if they don't get it fixed immediately.
Apple literally has zero power in this situation, as Verizon doesn't care if every iPhone owner returns their phone and buys one of the old iPhone 11s many Verizon offices still has in stock, or an Android any more than your local gas station owner cares about what model of car you drive.
What you are asking is akin to having Sony come out and make sure their televisions are compatible with every television station in the USA; no, they build their TVs to meet the appropriate ATSC specs.