this is just my headcanon but i really like to think that COH's sheikah stones are echo's era public transportation
like they are very clearly sheikah made(probably by lueberry) but they are also spread just about everywhere
(the squares with the little blue gate have a sheikah stone and thus can be teleported into)
not only every important location in COH(lake hylia, gerudo village, the windmill,kakariko, lost woods's entrance and all of the dungeons and fate cabins and fairy fountains) have a sheikah stone on it but they are also just spread all over hyrule and while yes several of them are just in nowhere i think its valid to point out that 1:COH's map is far smaler than EOW's map and exclude places who absolutely would have atleast 1 sheikah stone(probably more) like goron village and zora's domain and maybe the 3 temples dedicated to the golden godesses
2: Lin has stated that Hyrule's map was canonically scrambled during the events of COH in this post so lots of these sheikah stones are probably out of place
i also dont think this is anything exclusive for Echo and Silent, in cadence of hyrule in order to warp towards a sheikah stone your current character plays a tune on a lute, now not only the lute is seemingly a normal lute but when you consider who gives you the lute...
is cadence herself who is not even from Echo's world(she even admits to using the sheikah stones to get around hyrule before giving it to you wich clearly proves that basically anyone can use it, infact even Yves who doesnt have arms on account of being a deku scrub is able to play the lute and warp across sheikah stones despite being unable to use most of echo and silent's items)
as for why they are deactivated at the start of the game its simple:its a contingency to stop invaders from using it
at the start of the game both echo and silent have been taken down and placed into a cursed sleep by octavo, lueberry cant really stop octavo himself... but he can shut down the sheikah stones and make it harder for octavo's armies to get around