Why tube rectification?

This question is directed at the distinguished members of the forum who design and build tube amps or those who have knowledge of tube amp design. All the tube amps I own/have built us two diodes for rectification. Diodes are cheap, compact and last the life of the amplifier in most cases. Examples include the Dynaco ST-35, the Decware Zenkit1 (which is basically a Decware SE84) and the Elekit TU-8900. All reasonably well respected amps. Yet many of the more expensive amps go with tube rectification, which obviously involves the downside of another tube, more power, more space.

These two competing solutions both supply the basic power to the audio tubes and output transformers, so only indirectly interact with the sound signal. I have not read anything that explains what tube rectification brings to the party. But it must have some upside to offset it's obvious downsides. If I changed over one of the above amps to tube from diode rectification what would I be likely to  hear?