Some interesting and valid points
Flash colour output does vary. With the "budget" brands that only used one (or sometimes two) capacitors, it varied a lot. Historically, flash heads could only be set to a choice of full, half or a quarter power, this normally meant that the flash head had 4 capacitors, all used at full power, two used at half power and one at quarter power, and that was fine. but marketing created a "need" for a wide and infinite range of power settings, and this basically involved including a potentiometer into the system, which caused massive colour shifts, and especially at low power settings, and the cheaper the lights, the worse the problem . . . I remember testing one very popular American brand that shifted 1200K between max and min power, but these were marketed to people who didn't even see the problem
Move forward, and now we use IGBT flashes (mostly) and the problem no longer exists in real terms, because IGBT flashes always fire at full power regardless of the setting, at lower settings the flash is on for less time.
As for yellowing of the softbox fabric, we've had this problem ever since Chimera invented fabric softboxes (before that they were metal boxes with ground glass screens). Chimera were excellent but very expensive (and the Bowens Wafer weren't that far behind them) and we always had to correct this yellowing, and a hint of blue spray paint was the normal professional cure.
But, I'm talking about high-end professional work. I specialised in product photography, and colours needed to be spot-on, especially with fashion, for obvious reasons, and especially because, back then, everything ended up in print, so it had to be right.
Fast-forward to today, very little gets printed and nearly everything is viewed on computer, and the average viewer doesn't have a calibrated monitor, so colours are all over the place, nobody notices and nobody cares. Two of my monitors are calibrated correctly, the third one is a cheapie that I use just to keep my tools or documents, the colours are hopelessly wrong, and sitting here and moving a photo from one of the calibrated monitors to the 3rd monitor shows just how far off it is.
So, that's my long answer. My short answer is that whether the colour shift matters or not depends on a lot of different factors, and what matters to one person may not matter to another.