Why is the order of brainwaves not labelled "alphabetically"? The brainwave - frequency breakdown is as follows:


Delta wave – (0.1 – 3 Hz)
Theta wave – (4 – 7 Hz)
Alpha wave – (8 – 15 Hz)
Mu wave – (7.5 – 12.5 Hz)
SMR wave – (12.5 – 15.5 Hz)
Beta wave – (16 – 31 Hz)
Gamma wave – (32 – 100 Hz)


Just looking at the greek names, we're going: delta, theta, alpha, mu, beta, gamma (in order of ascending Hz).

Why don't we just relabel them as: mu(0.1-3Hz), theta, delta, gamma, beta, alpha(32-100Hz)? This seems to make more sense to me because the names are now ordinal, like the greek alphabet. Is there a reason that neuroscientists don't care about the order of the greek alphabet?
They are ordered based on when they were discovered/named (as pointed about by Ana's comment). Alpha and beta waves were among the first signals observed in EEG data. From Wikipedia:


  Alpha waves were discovered by German neurologist Hans Berger, most famous for his invention of the EEG. Alpha waves were among the first waves documented by Berger, along with beta waves, and he displayed an interest in "alpha blockage", the process by which alpha waves decrease and beta waves increase upon a subject opening their eyes. This distinction earned the alpha wave the alternate title of "Berger's Wave".


Hans Berger documented alpha and beta waves in a series of articles from 1929-1933.

Gamma waves took a few more decades to identify, because the higher frequency necessitates faster sampling. The earliest EEG systems were unable to measure oscillations at such fast frequencies.