Yes, he does have that authority, and I think that's what he's working towards. I can't remember the particulars but I remember Tim Gordon (or maybe it was Timothy Flanders/The Meaning of Catholic crew?) explaining how and why he has that authority, and this is coming from people who are on the side of the Latin Mass.
If it were outright banned I think you'd see multiple fractures in the TLM community.
1. You'd have those who are traditional who were already fully committed to recognizing Francis' papacy, they would pray and fast on behalf of the TLM but they would obey his decrees and go to a novus ordo. Either because they don't want to go through anymore drama or they just have no alternatives near them.
2. You have those who recognize Francis papacy and his authority but they look for a valid and licit alternative because they don't want to cave to the pressure to attend a novus ordo so they seek out either an Ordinariate parish or an Eastern Catholic Church.
3. You have the group that he probably had in mind when he first wrote Traditionis Custodes: those who are on the fence about Francis' papacy, or outright reject it (sedes, Benevacantists, Beneplenists, etc). Those are the ones most likely to start going to an SSPX chapel, or even go into full schism and seek out something else like the SSPV.
Basically in the wake of Vatican II the Mass of Paul VI (AKA the novus ordo) had a lot of momentum and in it's implementation bishops essentially squashed the TLM. It wasn't banned, Benedict XVI said specifically it was never abrogated, but it basically faded because the bishops took advnatage of people's ignorance and made people think it was. But there were still a few devotees out there, like Abp Lefebvre who founded the SSPX, they kept the TLM alive until the "indult era" began in the 1980s. That was essentially when TLM's began to emerge again but it was a complex process of having them approved.
That lasted until 2007 when Benedict XVI issues Summorum Pontificum, which said that any priest could celebrate the TLM if they wanted without the permission of their bishop. Now in 2021 Francis issues Traditionis Custodes, which reversed Summorum Pontificum and more or less returned the TLM's status to the indult days. But now he's going further and trying to kill it forever.
Me too. There are a lot of novus ordo bullies out there who try to accuse Latin Mass devotees of having too rosey of a perspective on the Latin Mass, pointing to the issues that plagued TLM parishes in the pre-conciliar era. They'll shutter in horror when describing a "bad" Latin Mass like someone shoved them into an iron maiden and made them read Chaucer.
The fact of the matter is, you're right. The TLM is intrinsically beautiful because it's intrinsically Catholic, the novus ordo is not because the novus ordo is intrinsically protestant. They drew all their styling cues from protestant modes of worship (which is all based on the "four bare walls and a sermon" philosophy), that's why your average diocesan parish is a outdated and mundane building with little to elevate the soul while a traditional parish features all of the elements that have been intended and used throughout salvation history to help us enter into worshiping the God of the universe.