In modern western modes, Ionian seems to be arbitrarily assigned as 'mode I', while the remaining modes are numbered according to the scale degree their tonic is relative to Ionian of same key.
For example, changing the tonic of the all naturals key signature from C (C Ionian) to the second degree D gives you the Dorian mode, and as such Dorian is referred to as 'mode II'.
From this convention the modes are ordered as:
I - Ionian II - Dorian III - Phrygian IV - Lydian V - Mixolydian VI - Aeolian VII - Locrian
I understand that Ionian (from Major) is one of the most common modes in western music and as such it would make sense to stem from that, however to me it seems to be more logical to order the modes based on adding sharps / flats to the key signature of a scale, while the tonic remains the same.
For example, starting from F Lydian (natural key signature) if I add a flat to the key signature (shifting down on the circle of fifths) while beginning the scale on the same tonic I get F Ionian. The reason I start with Lydian here is because sharpening the key signature would sharpen F and thus change the tonic. Continuing to flatten the key signature yields this order:
0 - F Lydian (Natural) 1 - F Ionian (1 flat) 2 - F Mixolydian (2 flats) 3 - F Dorian (3 flats) 4 - F Aeolian (4 flats) 5 - F Phrygian (5 flats) 6 - F Locrian (6 flats/6 sharps)
Of course you could follow the same pattern with another note as the tonic such as D, which would give the key signatures 3#, 2#, 1#, natural, 1b, 2b, 3b however the order of the modes would remain the same as above.
Ordering modes by how 'flattened/sharpened' they are (for lack of better term) seems to give the advantage of making more logical sense as to the order and relationship between the modes, as well as allowing another way to figure out the key signature given a tonic and mode eg. going from Ionian (1) to Phrygian (5) is as simple as flattening the key signature 4 times. Why isn't this approach to modes the norm, compared to thinking of modes as shifting the tonic of Ionian?