You can implement this feature. There is no technical barrier: you can write the log information to a file, and have a http end point similar to /jl and /db to print out the log information. Probably the biggest constraint is that there is not much flash memory space: there is only a total of 2MB spare flash memory, which has to be shared by the data files, regular log files. The more debug log file takes, the less space it is there for the regular log files.
Another option is to send debug information through MQTT: as the firmware already supports MQTT, just set up a MQTT broker on some computer, and send debug information through that. This takes no flash memory space and is relatively fast.