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After they assemble wheels they use a machine (or human) to adjust the spokes until the rim doesn't wobble. If the hub were manufactured out of true - and it sounds like it was - it would be cancelled out by the spoke truing.
Probably still rideable. Depends how bad and it is and how much you care how it looks.
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It’s pretty noticeable, to the point I’d rather have it replaced than spend more time doing hub services in a few months. Actually, would this 2mm off centre wobble affect the load on the bearings, spokes, rim? Its noticeable but I don’t want to sink much more time into it, unless it means leaving my MIL with a subpar wheel that will break down. I can’t say for certain without my glasses but it all looks built symmetrical enough, except it’s not.
Eseman
Why would the hub wobble on the drive side of a new 700C rim brake rear wheel if I hold the wheel by it’s axle and spin it, but the rim spins round and true?
I replaced the axle so I don’t think it’s that. If it were I would expect the rim to wobble as well.
The bearings are all in place. The cones and nuts are nicely tightened. I’ve triple checked, and removed the dust caps so can confirm.
If the wheel was assembled wrong, wouldn’t the hub spin true around the axle, and the rim would wobble?