A lot of scholars have written about the myth, though not necessarily in the granular detail or from the same angle that Liberman did. I think that more has been written about Loki which touches on the Baldr myth than works which are specifically about the Baldr myth. Here are some that come to mind, and they all have references to others.
Jens Peter Schjødt mentions it throughout his book Initiation Between Worlds: Structure and Symbolism in Pre-Christian Scandinavian Religion. He's mostly concerned with looking at the relationship between the world of the living and the world of the dead, so those are the aspects of the myth he focuses on. Schjødt has more experience writing about Loki than about Baldr, but of course you can't write about one without the other.
Kevin Wanner, best known for writing Snorri Sturluson and the Edda: The Conversion of Cultural Capital in Medieval Scandinavia, wrote an article called "Cunning Intelligence in Norse Myth: Loki, Óðinn, and the Limits of Sovereignty," which is mostly about the relationship between Óðinn and Loki (including the Baldr story), and the relationship of the pair to human people, especially poets. It takes a little while to get to the point, but I think it's worth it.
Anyway, to the second part of the question, I'd rather get kicked in the solar plexus by a mule than watch a YouTube video so I'm not going to comment on what Crawford says there specifically, but the "Loki doesn't have any place-names" argument is old and usually comes in two varieties. If Crawford came up with a third, then I apologize for the oversight, but I imagine it's one of these:
- (the good one): We know from the sagas that naming places for gods was a common way to show devotion, and from archaeology that many places named for gods were important ritual centers; furthermore places named for gods tend to concentrate near centers of social and political power. Therefore, if we're able to demonstrate that place-name evidence was passed down reliably from medieval or earlier times, it can be one of the strongest indicators available to us of cultic activity directed toward specific named gods and its presence allows us to make much more confident statements about worship than we can make in their absence. While this is inherently limited, because it necessarily privileges the beliefs of the people who had the social position to declare names of places and to direct the construction of ritual sites, it's one of the best pieces of evidence available to us.
- (the bad one): oh yeah, no, if they don't have any places named for them they weren't worshiped. Yeah, they definitely would have named a place after him and it definitely would have been unchanged until modern times. No, there were no other forms of devotion, just naming stuff.
I don't recognize the statement "the evidence does not permit us to say that there was a cult of Loki" as equivalent to saying "we can say definitively that there was not a cult of Loki."
Moreover, I think it's a failure of imagination to think that all devotion would take the same form. I don't imagine that Loki's idol was ever on the highest platform in a major ritual site like Thor's was at Uppsala but that's also not a useful standard, and it seems to me that it's the standard that the place-name argument holds him to. If we look at the Baltic peoples for comparison, they had very different forms of worship for different gods, so the absence of evidence for worship of Žemyna in a context appropriate for the worship of Perkūnas does not mean that Žemyna was not worshiped.
Anyway these days everyone seems to be on the "Loki was just a regular house spirit for many generations before being assimilated into the gods" bandwagon, one that I have disagreements with, but one which is compatible with "Loki was worshiped but not in a way that would result in place-names." Liberman made a case for Loki being a very, very ancient god; and Riccardo Ginevra's etymology of Sígyn requires that Loki's wife already be thousands of years old by the Viking age. There's lots and lots and lots of ways to argue in favor of him having been worshiped, all of which require modification of the word "worship" from the one the place-name-arguers use, so that eventually everyone is talking past each other. At the end of the day, "We don't know" is the actual answer to most of our questions.