First I will attempt to explain the two methods Fender used to bias amps.

Don't go into the amp if you don't know how to discharge filter caps or work around high voltage! When you bias an amp, the amp is running with full voltage and can seriously hurt you!

Contrary to what it sounds like, fixed bias amps are the ones that need their bias checked even more than others. Fender started to use fixed bias in the mid to late '50's. Amps Fender made that are fixed bias include the tweed Twin and Bassman, tweed Super/Pro/Bandmaster, all brown amps, all blackface amps with the exception of the Champ and Vibro-Champ, all silverface amps with the exception of the Champ, Vibro-Champ and Bronco (although in the early silverface years some amps had both cathode and fixed bias). Without going too far into it, fixed bias is a better way to bias the amp if linearity and lower distortion is desired. With fixed bias, the amp will run away and burn up the power tubes if the bias supply is lost or adjusted wrong. When you install new tubes in a fixed bias amp, you need to make sure that the amp is biased right. If it isn't, you could either be exceeding the wattage that the tubes can safely run at, wearing them out very quickly, or running them too cold giving bad tone. New Fender amps are almost always biased cold. This is not because they want you to have bad tone, but because it is safer for them to sell amps this way. There is less chance that the amp will be running in the "red". This reduces failures and warranty repairs! In the real world, these amps will run fine with a bit hotter bias, but this would require too much time and labor to bias them correctly at the factory for Fender to keep the amps at the price that they are.

The only reason you WOULD NOT have to check bias when changing tubes in a fixed bias amp is if you originally bought twice as many matched tubes as the amp uses and had the amp biased when you used the first set. The second set that you use when the first set wears out will be the same tubes, so the amp doesn't need to be biased. This is a handy trick if you go through a lot of tubes (like if you play very often). If you use a 2 6L6 amp, you might want to buy 4 or 6 matched tubes. When it's time for new tubes, just plug in the new ones.

Cathode bias is different than fixed bias. This way, current is limited to the tubes with a big resistor on the cathodes of the power tubes. In this respect, the power tubes are biased similar to the way the preamp tubes are biased. This is the reason why you can just plug in new preamp tubes. Cathode biased amps aren't as affected by different tubes. BUT, it's still a good idea to check the bias on these amps! If you get tubes that are far off the specs of the ones that were in the amp, the cathode resistor may need to get changed. The cathode resistor can drift in value after many years of use as well. This could change things. Usually, you can assume that cathode biased amps are just fine to plug new tubes into. However it's not a bad idea to have a tech make sure it's running fine.

Biasing your amp is way to optimize tone and maximize tube life. In extreme circumstances, the amp could be on the verge of meltdown if you just plug in new tubes without biasing. My Hiwatt is a good example of this. With the Tesla tubes that came in it, the amp was biased too cold. When I stuck in a pair of Svetlanas, the amp was way too hot! The amp was seriously on the verge of meltdown. I bought a load of a certain type of NOS tubes to match a while back, and even with NOS there is a pretty big difference in the way that they idled among them. It happens folks. You need to get your amp checked when you get new tubes. If not only to save your tubes and possibly other parts that might go with the tubes, do it to optimize tone.