[citation needed]

My understanding is that it was just a printing convention because þ was unavailable in movable type at the time, with y being the closest approximation. Y was never pronounced like th except when it was understood to be substituting for thorn.

Wikipedia:

With the arrival of movable type printing, the substitution of ⟨y⟩ for ⟨Þ⟩ became ubiquitous, leading to the common ye as in “Ye Olde Curiositie Shoppe”. One major reason for this was that ⟨y⟩ existed in the blackletter types that William Caxton and his contemporaries imported from Belgium and the Netherlands, while ⟨Þ⟩ did not, resulting in yͤ as well as ye.