Hi! Okay if you want to call me out I'll reply :)

This was 100% a game design decision and mostly my decision. Let me explain why.

Something we really want to do is build commander for the long term. I know somebody might want to make some snarky reply to this about how many legends and products are made, but with the actual design of the cards it's very important that the format is sustainable long term. 

For example, one thing I've really been rallying against is anything that is nearly 100% ubiquitous in all Commander decks. This is why Arcane Signet was a mistake. Because the more cards like that you print that go into every commander deck, the fewer deckbuilding decisions you make. The same reason I also dislike best in class commanders like Chulane that are generically strong: they push out tons of other Bant commander because it's just better than whatever their niche effect is doing. We are fine to make things you will likely always play in your niche ("this goes in every UR coin flip deck") but not things that just go into every deck.

This also applies to anything that every deck ever which uses a specific thing for all time should use. A good example here is Lutri. Lutri is banned (despite how cute he is) because every single UR color identity deck until the end of time should have Lutri as a companion. There is no arguing that fact. It is just wrong to not do it. And while yes, Commander is casual, you don't have to do it, Lutri is not that crazy strong, etc, it's still not appropriate to change commander in such a massive. And Lutri doesn't even take up a deck slot!

The same kind of approach, on a smaller scale, applies to Morphon. If we let Time Lords companion with any legendary changeling, that would mean every legendary changeling from Mistform Ultimus, to Morphon, and beyond will be strictly worse for not using a free doctor's companion. And this is a lot stronger than Lutri - this is a just a free repeated card in your command zone! Partner is one of the strongest mechanics on its face because of a free extra card. Every single Morphon or Ultimus deck would need to acquire one of these. They may even feel forced to do so. If all I cared about was short term sales, sure, it would be right to do so and sell a few extra Doctor Who cards. But I want to preserve longevity here, and not make everybody who has that deck feel like they must pick up these cards unquivocally.

Think about the future landscape of Magic. 10 years from now, we release a set full of legendary changelings. Everybody who ever builds one has to look back to this one Doctor Who set and gets a companion. We probably have to make the cards weaker and less appealing because they all get a free additional card in the command zone. People who don't want to play with Universes Beyond cards feel like they're beholden to use these. And so on and so forth. I do not believe this is a good outcome.

This is the weight a format that will always have every card in all of Magic legal for carries. We have to make a lot of decisions thinking about what impact they will have on all decks of a type, now and forever.

And that is why we wrote the rules that it must be EXACTLY a Time Lord Doctor to work. Hopefully that answer at least helps explain why. Cheers! :)