The physical SIM numbers are infrastructure that we built, using racks of GSM modems, SIM card switching devices, and our own software to manage everything. The SIM card switching devices reduce maintenance requirements since when a customer no longer needs a SIM, we can electronically switch the modem to a new SIM without needing to visit the datacentre. We just have to go every so often to replace the used SIMs before the pool runs low.
From the perspective of a number verification system (or anything else sending an SMS to them), they are completely indistinguishable from a mobile phone and prepaid SIM, since that is what they are.
The virtual numbers, while also never re-used, are often blacklisted by services that do SMS verification due to coming from a range designated as "VoIP" or "virtual", and we explicitly disrecommend their use for verification, although some people do use them with varying amounts of success since they are cheaper than the SIM numbers.
This isn't true; UK mobile numbers are re-used after a period of inactivity by the operator themselves.
Unless, of course, you're keeping the number/line live in permanence? But I can't see how your service would make that work financially.
Of course unless phone numbers perpetually get longer, they have to eventually get re-used. We don't implement any re-use but the operator will indeed eventually recycle them.