RCA 630TS Transformer Question

[BelowZero]

Looking at the RCA 630TS power transformer wiring diagram I find that the 6.3 heater voltage is supplied by a center tapped 12.6 winding with one wire marked X and the other wire marked Y, with some tubes heaters fed by the X wire and other tubes including the CRT fed by Y.
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I'm working on a Fada 630TS clone chassis and the Sams schematic for that set shows the same 12.6 CT diagram as above. Some time in the past the power transformer has been replaced in this set, the replacement doesn't have the 12.6 CT winding, instead it has a 6.3 winding without a center tap, one wire grounded and the other wire feeding all of the 6.3 voltage to the tubes.
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The set was working with this replacement transformer but my question is would it be better to use a transformer with the 12.6 CT winding? I suppose the 6.3 winding in the replacement would be OK if the amp rating is high enough, Sams shows 5.1a for the 12.6.

I would like to learn what was the advantage of splitting a 12.6 winding to get the needed 6.3 heater voltage?