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Just as busy if not busier for the non JR lines.

But don’t worry about getting off and on the trains too much. When you arrive at the ticket gates you should ask for assistance. Someone will then escort you and there will then be someone to greet you when you arrive.
They’ll take care of getting your mum on and off the trains (so long as it isn’t rush hour). Do please realise that these assistants are unlikely to speak any English. Perhaps keep a map on you to point out your route.

So rather than worry about getting off and on a train, think about how you might get to the station ticket barriers. Here’s a random taste of a walk through Ikebukuro to show what I mean. And this is not a particularly busy time: