I say no. What say you?
No but you need to tell your client why.
I would say no also, and would explain that mixing low voltage and high voltage wiring mix is not allways conducive due to overheating, touching of the different voltage wiring, and mostly that it is not a part of the listing of the Electrical panel and does not belong in there.
It should be installed to a nearby receptacle box. 
Heat, wrong current, wrong load side conductors to be in the panel, not service equipment. I would go on, but in the middle of the inspection.
Heat is not the issue.
The secondary of that transformer is Class 2. Class 2 conductors cannot occupy the same enclosure as power conductors.
Exactly!
What is a class 2 and why can’t they occupy the same enclosure as power conductors?
The NEC prohibits them together because Class 2 condcutors can be run differently than power condcutors and if the power condcutors were to impose a higher voltage on the Class 2 conductors there is a risk of fire or personal injury.
Class 2 circuits. Class 2 circuits typically include wiring for low-energy (100VA or less), low-voltage (under 30V) loads such as low-voltage lighting, thermostats, PLCs, security systems, and limited-energy voice, intercom, sound, and public address systems. You can also use them for twisted-pair or coaxial local area networks (LAN) [725.41(A)(4)].
Been like that for years.
No mixing.
I have used cableways with separations before also. Most had their own conduit and completly isolated from each other. There is a reason, not mine to know why, just part of knowing that they do not mix.
Gotcha because class 2 doesn’t need ocpds so if even a 14 ga conductor energizes the class two conductors from the door bell wiring, there is nothing to stop it from overheating and causing a fire?
Think of the remote possibility of those 120 volt conductors energizing the 24 VAC secondary conductors. Now someone presses the door bell button, well then a lot of bad things can happen.
Seems like we are going back to what I iniatilly said.
" mixing low voltage and high voltage wiring mix is not allways conducive due to overheating, touching of the different voltage wiring, and mostly that it is not a part of the listing of the Electrical panel "
I was always led to believe that these transformers could not be enclosed. Is that correct? That is why I mentioned the heat issue.
Hey are you guys saying I need to pull the phone wire out of my main panel now.OH snap.
I agree the transformer should not be in the panel and always report it as such. However, going into great details as to why is way over the heads of most clients, so I just say that it is improper and let it go art that. If questions arise later ( has rarely happened ) I can explain in more detail.
I agree. No need to include class 2 wiring descriptions/comments in a report narrative. Its just plain not part of the service equipment.