Would the iii be a substitute for I under such circumstances or does iii make another deceptive resolution kind of like when V progresses to vi? iii also has ^3 and ^5 which belong to tonic harmony but since it doesnt have ^1 I cant say it sounds the same as when V goes to vi.
There are rules. Some people even follow them.
In C, a G7 resolving to e would likely have an F resolving to E, but the B doesn't resolve to C, so the tritone resolution feels merely half-satisfying. If you instead have a three-note G chord resolving to e, the only note that needs to change is that D moves to E. This would feel much less like a resolution.
Entire eras are defined by how they fail to resolve the V chord. V -> iii would not be an earth-shattering addition to the canon.
iii Could never (or rarely) be a substitute for I, because iii loses the tonic and changes it for the leading tone, which makes the chord minor and less stable, while I is major and stable. (Talking about major tonality)
In the other hand, iii could be a substitute for vi, because they both are minor and share one important tonal degree (iii's third (dominant) and vi's third (tonic) which makes them sound similar. They give the same feeling of 'unfinished' that is used in interrupted cadences.
(Remember that even though iii and vi sound similar, interrupted cadences finish in vi (V-vi) This happens because the leading tone of V leads to the vi's third (tonic).This also happens in V-I resolution. This way, vi sounds more like 'I' that iii does.