The solderless breadboard itself has small conductors internally, they are designed for small signal prototyping, and have rather high resistance compared to the soldered, wide tracks on a pc board.
The wire size isn't as much of an issue as the voltage fluctuations while switching higher powered loads on and off. Logic ICs, op-ams, microcontrollers, and even analog circuits tend to not work right when the voltage drops when the output is switched.
The power devices should be at least on a separate solderless breadboard with an independent large gauge wire path to the power supply, not daisy chained to the first breadboard. This isn't an option for TO-3 package devices, so a "spare" TO-3 holder with 22ga wires to go to the breadboard would work for prototype verification, but not long term usage. With 1 foot of 22 gauge wire, about half a watt would be dissipated in the wire alone at 7A, about a 0.1V drop, not counting the resistance of breadboard connections.