Vaškaninová et al. 2020
employ several partial placoderms from Czechoslovakia to demonstrate the antiquity of lingual tooth growth (= from the inside out as in modern fishes; Fig. 1).
Unfortunately taxon exclusion mars this study.
Following tradition, the team thought derived placoderms (in the process of losing their teeth) were primitive taxa just gaining teeth (Fig. 1). Like other workers before them, they omitted too many taxa.
By contrast and using a wider gamut of taxa,
we looked at the origin of marginal teeth earlier here. Marginal teeth first appeared in the late-surviving basal paddlefish, Tanyrhinichthys (Fig. 2). The outgroup taxon, late-shriving Chondrosteus, (Fig. 3) lacked teeth and tooth-bearing bones (the premaxilla, maxilla and dentary).
From the Vaškaninová et al. 2020 abstract:
“The dentitions of extant fishes and land vertebrates vary in both pattern and type of tooth replacement. It has been argued that the common ancestral condition likely resembles the nonmarginal, radially arranged tooth files of arthrodires, an early group of armoured fishes. We used synchrotron microtomography to describe the fossil dentitions of so-called acanthothoracids, the most phylogenetically basal jawed vertebrates with teeth, belonging to the genera Radotina, Kosoraspis, and Tlamaspis (from the Early Devonian of the Czech Republic).
Note: In the LRT these taxa are placoderms in the process of losing their teeth. Teeth developed much earlier in the family tree (Fig. 4).
“Their dentitions differ fundamentally from those of arthrodires; they are marginal, carried by a cheekbone or a series of short dermal bones along the jaw edges, and teeth are added lingually as is the case in many chondrichthyans (cartilaginous fishes) and osteichthyans (bony fishes and tetrapods). We propose these characteristics as ancestral for all jawed vertebrates.”

Figure 1. Omitting many pertinent taxa, Vaskaninova et al. constructed this cladogram of tooth evolution. The LRT uses a wider gamut of taxa and recovers a different tree topology. See figure 4.
In the Vaškaninová et al. 2020 study
basal fish, both jawless and not, are all armored.
Here
in the large reptile tree (LRT, 1707+ taxa) the origin of jaws lacking teeth is close to Chondrosteus (Fig. 3), a derived sturgeon (Fig. 10). In Chondrosteus the upper jaw is the lacrimal. The premaxilla and maxilla have not appeared yet. The lower jaw likewise lacks a dentary and is composed of the surangular and angular.

Figure 2. Skull of Tanyrhinichthys (above) with two bones relabeled. The other fish, Saurichthys, is clearly unrelated. The origin of tiny marginal teeth is close to Tanyrhinnichthys, a basal paddlefish (Fig. 2), the next moreb derived clade in the LRT. The tooth bearing bones (premaxillla, maxilla and dentary) originate as slender dermal layers on the lacrimal and surangular carrying tiny teeth, not much larger than skin denticles.
Adding taxa in the LRT
separates armored Devonian placoderms from armored Silurian jawless fish.

Figure 3. Chondrosteus animation (2 frames) in situ and reconstructed in lateral view. This is the transitional taxon linking sturgeons to bony fish + sharks.
Chronology is not as helpful as phylogeny
in figuring out these transitions, so much so that extant taxa need to be added to fill out the tree topology (Fig. 4).

Figure x. Subset of the LRT, focusing on fish for July 2020.
Members of the Placodermi
like their relatives the catfish, are relatively derived taxa in the LRT (Fig. 4). Marginal teeth are missing in catfish and placoderms because they both have lost the maxilla along with their last common ancestor, taxa near late-surviving Diplacanthus.

Figure 5. Radotina is a basal taxon in the Vaskaninova et al. cladogram (Fig. 1). Compare to Romundina (Fig. 6) another basal taxon in Vaskaninova et al.
Basal taxa in the Vaskaninova et al. cladogram,
Romundina (Fig. 6) and Radotina (Fig. 5) are rather specialized terminal taxa in the LRT, leaving no descendants. Chondrosteus and Tanyrhinichthys are more generalized and primitive. All living fish, other than sturgeons (Fig. 10), whale sharks and mantas, are derived from Silurian sisters to these two taxa in the LRT.

Figure 6. What little we know of Radotina and where the same bone appears on the more complete Romundina, a terminal taxon in the Placodermi.
Vaškaninová et al. provide the parts for Kosoraspis
(Fig. 7), a basal taxon without resolution in figure 1. Here (Fig. 8) I provide a possible restoration in which the large curved green bone identified as the ‘preopercular’ is re-identified as a postfrontal (orange in Fig. 8) based on similarities to Clarias, the walking catfish (Fig. 9).

Figure 7. From Vaškaninová et al. 2020, the parts for Kosoraspis. See figure 9 for a reconstruction where the largest bone here (green preopercular) is relabeled a postfrontal.

Figure 8. Kosoraspis restored as a Devonian catfish like Clarias (Fig. 10). Those tooth plates are similar to those in catfish.

FIgure 9. Clarias, the walking catfish is a living placoderm with skull bones colorized as homologs of those in Entelognathus (Fig. 2). Here the mandible shifts forward and the opercular shifts backwards relative to Entelongnathus in the Silurian.
Determining when teeth and jaws first appeared
in basal vertebrates has been a contentious issue largely because pertinent taxa have been left out of the solution. Apparently Vaškaninová et al. left out several taxa key to understanding this transition from toothless jaws to toothy jaws. They considered taxa in the process of losing teeth, but placed them at the genesis of developing teeth.
Once again,
more taxa resolve problems like this better than more characters do.

Figure 10. Top to bottom: Thelodus a soft jawless fish with a ventral oral opening and gill slits, perhaps a hint of diamond-shaped armor laterally. Hemicyclaspis, adds extensive armor. Acipenser, a sturgeon with a protrusible tube for a mouth and reduced armor.
If this helps,
here again (Fig. 10) are three taxa preceding the origin of jaws with marginal teeth. These interrelationships have gone unnoticed by fish workers who continue to nest sturgeons with jawed fishes. The next taxon following these three had large jaws: Chondrosteus (Fig. 3).

Figure 11. Manta compared to Thelodus (Loganellia) and Rhincodon. All three have a terminal mouth essentially straight across, between the lateral eyes, distinct from most fish. Note the lack of teeth.
Here again are whale sharks and mantas
(Fig. 11) on their own branch derived from Silurian sisters to Thelodus and Loganellia. These taxa have jaws, but lack marginal teeth, similar to Chondrosteus (Fig. 3).
As mentioned above,
it is so important to include a wide gamut of taxa, including extant taxa.
References
Vaškaninová V, Chen D, Tafforeau P, Johanson Z, Ekrt B, Blom H and Ahlberg PE 2020. Marginal dentition and multiple dermal jawbones as the ancestral condition of jawed vertebrates. Science 369(6500): 211-216 DOI: 10.1126/science.aaz9431
https://science.sciencemag.org/content/369/6500/211
placoderm jaws
News:
https://phys.org/news/2020-07-advanced-technology-evolution-teeth.html