Opener rebidding 1S only if he is unbalanced and 1NT with all balanced hands--4333, 4432, and 5m332; no singletons--even if he has four spades, leads to easier auctions and wins more times than it loses.
Admittedly you will lose if responder also has 4 spades and less than an invitational hand. But my guess is that responder having 4 spades in addition to his 4+ hearts is not common (25% or less?). Since responder must also be less than invitational, that drives the probability even lower. Moreover, when opener rebids 1NT with 4 spades and responder does not have 4 spades (which is the more frequent situation), you get wins sometimes: you get a lead into your spade suit, or maybe the opponents balance into spades after 1D-1H 1N because spades are safe.
Consider the follow ups based on responder's heart length.
If responder has 6 hearts, it's easier and more accurate to rebid 3H and 4H over 1NT than over 1S. Over 1S, you need to worry about that small singleton or void in opener's hand. Not so over 1NT. And since responder knows that an 8+ card fit exists in hearts, sometimes responder can make an invitational bid over 1NT when it would not be right to do so over 1S.
If responder has 5 hearts and less than 4 spades, responder has an easy rebid over 1NT regardless of strength assuming you are playing almost any type of new minor forcing, two way new minor forcing, or whatever). And if opener has only 2 hearts, you will wind up playing 2H when opener is minimum. On the other hand, after 1D-1H-1S, if 2C is game forcing, you may miss a 5-3 heart fit when opener is minimum and responder is invitational. If 2C is a one round force, you will wind up playing 2NT when opener is minimum and has only two hearts. Simulations show that the 5-2 fit plays better. If 2C is neither, you have other problems.
If responder has 5 hearts and 4 spades, you will find the 4-4 spade fit whenever responder is invitational or better. So the only time you lose is with this distribution is when responder is less than invitational. But if responder is 5-4, it's 2-1 it isn't spades.
If responder has exactly four hearts and is balanced, the rebidding is easy whenter your rebid 1S or 1N.
If responder has three hearts (not a typo), 1NT enables getting to 2D or 3C easily.
1S showing an unbalanced hand with 4 spades means that 1NT will not be passed. So with
♠xx
♥xxxx
♦xxxx
♠xxx
rebid 1NT and opener will bid 2m in his 5+ suit unless he is exactly 4-4-4-1.
Klinger has suggested this approach (1S only with unbalanced hands) in natural systems. With Precision's ambiguous 1D, it seems even more useful. I have sometimes wondered whether it would be even more useful to have a 1S rebid show any unbalanced 2- or 3-suited hand without 4 hearts. But I've never taken the time to work out the details.