Most builds can indeed get away with side-by-side routing of heaters wires. I've done it, and Sluckey has a photo of a beautiful build with such heater wiring. Hoffman doesn't bother with on his BJ tube board
https://el34world.com/Hoffman/Blues_Junior_Tube_Board.htm.
But it is also true that twisting your heater supply wires is less prone to propagating heater hum to nearby signal wires.
It's undeniable that twisting your heater supply is a mild pain. But I stress the term mild here.
I'm quite sure there are many ways to accomplish the goal. You could purchase Cat 3 UTP and liberate the twisted pairs from within -- these are normally 24ga solid. You may or may not be comfortable with 24ga heater wires, but -- recall the ampacity for these is stated for bundling purposes most often, and these wires are hanging out in the breeze and should not overheat.
Or, use the famous electric drill method for 22ga (what I use) or 20ga wires. I clamp two wires together in a vise, and then the other ends in my drill chuck. You have pull them tight enough so that the wires don't kink when you begin the twisting with the drill. Twist them tight -- and take care that they don't kink when you undo the chuck.
I have become a fan of routing heater wires at the lower back corner of the chassis. I orient the tube sockets so that 2-7 (octals) are at the back, and 9 is at the back for the noval sockets. This allows me to route the wire to the 4-5 straight across the top of the socket between the 1 and 9 pins. I have not had problems with this method, even in high gain situations. I'm not sayin' this is the best for everyone! It works for me.
I may look around for some fancy lamp cord, though.
Cheers.