[OLD REGGIE]

it was a pastoral letter from one equal church to another [...] Clement had no direct authority over the church at Corinth.

Bishops to not write "pastoral" letters telling their fellow bishops what to do; it is a severe violation of the Canon Law.

Forget for the moment that Clement did not tell anyone what to do. There was no Canon Law for more than 1,000 years nor was there a Papacy when Clement was Bishop of Rome.

Feel free to develop your own retroactive history. You cannot apply your Canon Law retroactively

[annalex]

There was no Canon Law for more than 1,000 years

On that, you are quite wrong. This is the relevant canon from c. AD 400:

35. The bishops of every country ought to know who is the chief among them, and to esteem him as their head, and not to do any great thing without his consent; but every one to manage only the affairs that belong to his own parish, and the places subject to it. But let him not do anything without the consent of all; for it is by this means there will be unanimity, and God will be glorified by Christ, in the Holy Spirit.

36. A bishop must not venture to ordain out of his own bounds for cities or countries that are not subject to him. But if he be convicted of having done so without the consent of such as governed those cities or countries, let him be deprived, both the bishop himself and those whom he has ordained.

(Apostolic Constitution Book VIII)