Can you say what ordinary (non-discounted) pricing was like, per message? At least in the US, most carriers did I and, believe, still do operate free SMTP -> SMS gateways. They worked okay, although they resulted in oddly formatted messages.
Twilio has a public price sheet[1], I think they haven't actually updated this one lately, but it's a good representation of what ordinary pricing is like. This is not an endorsement (or non-endorsement) of Twilio, but having a public price sheet makes it easy to link to them.
In general, pricing varies widely by destination (country and sometimes carrier), US and some other places are < $0.01, up to $0.10/message isn't uncommon, and some places are $0.20-$0.30/message. Voice calling was usually mor expensive (Twilio should have a price list somewhere for that too; if you can get 6 or 1 second billing, assume a voice verification call is about 30 seconds, but you might have to pay for a whole minute even if you don't use a whole minute).
Those SMTP -> SMS gateways sometimes work in the US, but they don't work much in other countries, and they're not good enough to rely on if your product requires an SMS during the new user flow. SMS costs are real and it's frustrating, but if it costs too much, you need to use something other than phone numbers for ids; I don't think skirting by with email gateways is going to work. But, if you build dynamic routing, I guess you could try.
Also, you've got the use the right email gateway for the user's carrier, and a carrier lookup is on the order of $0.01, unless you have tons of volume, so for the US, you might as well pay for the SMS.
Oh I see... yeah, WA never went direct unless it was zero cost to us, so I don't know what carriers tend to charge. Managing payment to a foreign telecom would be challenging, managing it to enough carriers so the difference in cost is meaningful would be a major endeavor. SMS aggregation is a business with many providers and a low barrier to entry, so while there are margins, I don't think they're very high. There are some telecom groups that run networks in many countries, and some of those offer SMS aggregation services, and the prices were in the same ballpark as pure aggregators, as I recall, but it's been many years since I saw the price sheets.