FWIW, Replacing "th" with "θ" would really be a "re-placement": Theta and the "voiced dental fricative"[1] were smeared together in Old English long ago.[2]
I.e. "there" and "theater" are two different "th"'s.[3]
[3] English speakers: if you pay attention to how you speak those two words you'll notice that your tongue is doing different things to make those two "th" sounds. This is a weird "archaeo-linguistic" holdover in your "motor-culture". In a certain sense, "you" always knew this but didn't know you knew.
Icelandic still retains the Old English letters for voiced and unvoiced dental fricatives. Icelandic is said to be the closest modern language to Old English.
ð ("eth", voiced) and þ ("thorn", unvoiced). So you could write "ðere" and "þeater", for words that sound correct but don't make any sense in either language. :)
Fun fact, thorn is the reason for today's archaic phrase "Ye olde", which was always pronounced "The old". Print shops didn't have a thorn character, so they substituted y instead. https://en.wikipedia.org/wiki/Thorn_(letter)
* Kind of a tangent, but I'm also fascinated by Icelandic's unvoiced nasal fricative, a sound we don't have in English, and something that seems hard to do when you have a cold or runny nose.
Similarly, there's no letter for the voiced palato-alveolar fricative in English (and as I recall it's actually one of the newest sounds that is part of English). It's the voiced version of the "sh" sound -- an example is the "si" part of "vision".
It’s tellig that the first involves an archaic word no longer in use. And in my pronunciation (coastal California) the second pair differ in the vowel not the consonant. I pronounce them both as in “thy”.
"either" can be pronounced two ways in the first vowel, "ee" (like "eek!") or "eye" (like "eyeball"). Same as "neither". To compare with "ether" I'm assuming the first.
But "ether" can only be pronounced with unvoiced "th". If you pronounce it voiced, that would be very unusual. Are you sure? Check out:
I.e. "there" and "theater" are two different "th"'s.[3]
[1] https://en.wikipedia.org/wiki/Voiced_dental_fricative
[2] https://en.wikipedia.org/wiki/Th_(digraph)#Voiced_fricative_...
[3] English speakers: if you pay attention to how you speak those two words you'll notice that your tongue is doing different things to make those two "th" sounds. This is a weird "archaeo-linguistic" holdover in your "motor-culture". In a certain sense, "you" always knew this but didn't know you knew.