Its possible to build, but its just not practical.
Linear supplies weigh on the order of one pound per amp. and thats probably on the light side.
For alternative there is a switching power supply, but then your talking major $$ if you dont want RFI hash everywhere.
This is why tube amplifiers are used for base amps. because the transformer is stepping up voltage instead of the other way.
The 13.8v pills are at a major disadvantage because of the high current involved. The 2nd disadvantage is the impedance transformation from an ohm or less on the collector to get to 50 ohms.