Break in: I do believe that mechanical portions of your audio equipment (Speakers, headphones, microphones and maybe phono cartridges do benefit from a certain amount of break in over time. I prefer to refer to this as "settle in" time where a vibrating component tends to relax into its normal operating condition. Some items take more time, some less. I don't think this is a critical step as once use begins, this will take place anyway. Additionally, you may or may not even notice, or as one of my fellow professionals says, "you can get used to any speaker you choose to use." Some manufacturers even do this at the factory, before packaging, as just one more quality control step.
Amplifiers: The big improvements in amplifiers are the quality of the small parts, i.e. capacitors. resistors, transistors and FETs. Class A, AB, D etc., have not changed drastically recently but the afore mentioned improved component parts have allowed these designs to perform better.., but not to the tune of thousands of dollars more. The parts quality gains, mentioned, represent only small gains in the finished product's performance, the designs are basically similar to the same.
Tubes vs Transistors: It is true that there is a difference in sound between components built with either devices. There are many reasons not the least of which is the natural tendency of tubes to distort in a very pleasant way (even order harmonic distortion), while transistors naturally lean toward odd order harmonics, or not as pleasant. Also output transformers, in tube gear, have an effect on the final sound we hear leaning toward the warm, slightly boated, side. Again modern improved parts have begun to close this gap somewhat. Personally, I use solid state amps in my studio since they either work or they don't, and provide a long term reliable, unchanging reference. For relaxed listening, I prefer tube amps, or hybrids, but tubes, due to heat, deteriorate slowly over time.
Wire: This is a tricky one as it's been disproved as much as proved, through blind testing, whether the differences in wire can actually be heard. I am especially suspicious of a 6 foot AC cord getting rid of all the hash collected along MILES of power lines before entering your home. As I once told members of a local audiophile club " we couldn't afford to pay, $6 - $50+ per foot, what you guys are willing to spend for exotic wire.., we couldn't afford the rest of the recording gear for the studio. Typically, we run hundreds of feet." I got blank stares indicating a rejection of information both scientific and financial, in favor of mythical beliefs. OK!, moving on then. Ironically, the very recordings, highly revered, by these individuals are made with wires purchased in bulk rolls at roughly $0.33 a foot, or less, by manufacturers of pro grade cable. I rest my case.