It honestly doesn't simplify things over push notifications all that much. There are a lot of regulations if you are planning on having users in the US around A2P (Automated to Personal) messaging. You have to register a brand and transactional use campaign with TCR (The Campaign Registry - the regulatory body that manages this messaging), a process that costs money and can take months. They are capricious to say the least... So expect a lot of upkeep on your website, brand, campaign, and number usage as time goes on and they change regulations more or less on a whim.

As part of those regulations you have to deal with opt-in and opt-out formalities. It's a crime in the US to send a text message to someone in an automated way that they did not directly and concretely ask for. Doing so can result in heavy fines. Similarly if they opt out using any of a number of both standard and non-standard methods, you must comply with that even if it impacts their ability to use other parts of your system. You can work around that with multiple numbers, each attached to a different campaign of a different use-case, but do that too much and they'll get you for "snow shoeing" and it comes with more and more fines.

And on... And on... And on... This is my literal day-to-day job. I can say with relative confidence that if you are working with a small number of people, just use push notifications. It's actually easier.

Also, if you must go with SMS for whatever reason, your tier-1 providers, as you put it, will handle a lot of that regulatory guff for you (for a price of course), so don't look too far for other providers. If you want to own your own registered brand and campaign with TCR, then a good option is Telgorithm, although your integration complexity will go up pretty drastically.

Lastly, check your costs. Pricing for SMS is way more complicated than what the marketing language on provider websites seem to indicate. Talk with people doing similar things and get the real answers, and budget accordingly.