1) Sorry but this is false.
1a) That analysis is specifically for reducing QECC protocol to an entanglement distillation protocol over certain class of discrete variable channels. Exactly as in BDSW96. Task of the protocol is changed in the reduction.
1b) The simulation is not via a general LOCC but relies on teleportation (this is why you reduce the channel to the Choi matrix of the same channel)
1c) It does not apply to CV and asymptotic simulations (even with DV channels, see amplitude damping channel in PLOB15)
2) The result for discrete-variable covariant channels is prior to WTB17, due to Matthews and Leung [IEEE Trans. Inf. Theory 61, 4486 (2015)] not cited here.
For asymptotic simulations, both WTB17 and Wolf's notes cannot apply since there is no control whatsoever of the channel simulation due to the truncation of the Hilbert space.
3a) TW16, i.e., https://arxiv.org/abs/1611.09165 is a straightforward consequence of PRL 118, 100502 (2017), i.e., https://arxiv.org/abs/1609.02160 and PRL 113, 250801 (2014), i.e., https://arxiv.org/abs/1407.2934. TW16 use exactly the same methods, while trying to come up with different names. I mean for both DV and CV channels, i.e., including bosonic channels. All is included already in those two PRLs above.
3b) Here this specific paper on quantum reading considers adaptive channel discrimination in *discrete-variables*. The ultimate limits and teleportation methods were fully worked out in PRL 118, 100502 (2017), i.e., https://arxiv.org/abs/1609.02160v1. This is not even cited here. Why?
Sorry if I cannot be more positive but you should really try to give the right credit to previous literature while avoiding self-referencing as much as possible.
This is one of those papers where the contribution of previous literature is omitted and not fairly represented.
1- the LOCC simulation of quantum channels (not necessarily teleportation based) and the corresponding general reduction of adaptive protocols was developed in PLOB15 (https://arxiv.org/abs/1510.08863) not in BDSW96 or MH12 that only contained partial results. Both definition 2 and the reduction in proposition 2 of this Wilde's paper are heavily based on PLOB15 which is not credited here. On the actual status on channel simulation and reduction of adaptive protocols, see Supplementary Notes 8 and 9 in PLOB15 (https://arxiv.org/abs/1510.08863)
2- the statement that covariant channel implies teleportation simulability (Lemma 3) is also directly taken from previous papers, not Wilde's paper WTB17 (again the most general formulation of this statement was made at any dimension in PLOB15, again not credited here). Proposition 1 is another trivial consequence of PLOB15.
3- the simplification of adaptive channel discrimination via teleportation was first proven in Pirandola and Lupo PRL 118, 100502 (2017) on adaptive quantum metrology and channel discrimination, but this relevant literature is here omitted and Wilde's followup paper TW16 is credited. Note that TW16 itself is based on the PRL above, besides another previous PRL (by Lorenzo Maccone).
This is a nice result!