IMO....
1. Yes, Paul seems to suggest that baptisms done in any other name is ineffectual and divisive. The impression from the Book of Acts is that this is to be Trinitarian (with the Son being understood as Jesus, thus baptizing in His name).
2. I strongly suspect that Jesus made Baptize CENTRAL to The Great Commission (equal to the one other thing - teaching) .... Baptism plays such a major role in Acts and all the NT..... Baptism was regarded as very important from at least 69 AD to 1520 AD by every Christian..... because it's important. And it's important because because something happens through it. If it were a largely worthless thing.... or accomplished nothing.... it's hard to understand why Jesus would place it equal with just one other thing - teaching, hard to image why it would be universally embraced as SO important for over 1500 years (and still by the vast majority of Christians) if it was just an irrelevant waste of water. Consider: Jesus also washed the disciples' feet - and that was understood as purely symbolic - but it didn't get mentioned in The Great Commission.... it was not practiced in the Early Church.... because it was universally understood by all right from the start as symbolic and actually doing nothing (but getting manure off feet). It seems Baptism was regarded VERY differently than that.
3. There are two main Traditions about Baptism.
A. The orthodox, historic view dates from 69 AD at the very latest. I holds that Baptism is a "Means of Grace" (along with teaching - the other half of the Great Commission) which God may use to convey His blessings and gifts, "tools in the hands of the Carpenter" (to use the expression from medieval times). And that it is associated with faith and forgiveness. This view has no dogmatic prohibitions: none according to age, race, color, nationality, gender; no conditions of PREVIOUS "hoops" the recipient has done, no dogmatic prohibitions based on works. This view sees some connection to circumcision (done on infants.... without them first having to meet certain dogmatic mandates), a connection Scripture itself makes; and also a connection to the last of the Seven Plagues when parents embraced God's promise and by placing Blood, literally saved the life of their children (without the child needing to do or have anything; jumping through any hoops). This view has no prohibitions - noting Scripture has done. This view was universal from 69 - 1520 AD, and is still embraced by the great majority. I have a thread on this here:
https://christianityhaven.com/showthread.php?6945-Lutheran-Perspective-on-Baptism Also see
https://christianityhaven.com/showthread.php?7346-Baptism-Is-it-Innert-or-Effectual
B. The Anabaptists in the 16th Century invented another tradition. It claims there are several mandates and prohibitions that apply, although they admitted none of these are explicitely taught in Scripture and admit none of this was embraced for 1500 years before them; they admitted to inviting something brand new. They created 4 dogmas on this: 1) The recipient MUST attain a certain (unknown) age (Anti-Paedobaptism). 2) The recipient MUST first prove they have accepted Jesus as their personal Savior - usually a clear, consistent profession is sufficient (Credobaptism), 3) The recipient MUST first prove they have adequately repented of all their sins. They added a fourth that has to do with mode rather than prohibitions 4) Every cell of the recipients body must be entirely immersed under water (Immersion Only Baptism). Again, they said none of this is expressly taught in Scripture ... none of this was believed before them... but they imposed it anyway. They also tended to teach that Baptism is merely symbolic, "An outward sign of an inner decision" - although they admitted the Bible never actually says that. This view is essentially one of denial and prohibitions. Ironically, they spoke of the meanlessness of Baptism so much that their followers often became known as "Baptists."
I hope that helps.
- Josiah