Transfers are useful over 1N. They are even more useful over 2N or over 2C-2D/2N. While Jacoby (red suit) transfers are popular, 4 suit transfers are also coming into vogue. For example, 2S is often used as a transfer to clubs with 2N as either minor suit Stayman or a transfer to diamonds. Or 3C could be used as a transfer to diamonds.
Use of a transfer bid does NOT carry any suggestion wrt responder's point count. With a weak hand, responder wants to escape from notrump. Nor does it imply that responder has a one suited hand. This is determined when responder rebids a second suit, passes or raises the transfer suit.
Further (and I hope this is not straying from your question) advancer to an overcall may use transfers or responder may use transfers (rubensohl) when partner's notrump is overcalled.
And transfers enhance the communication process AND bring the limit bidder (the opening no-trumper) back into the dialogue. But breaking the transfer is allowed ONLY with a super "fit", when opener can jump to the three level; for the law of total tricks comes into the picture on the one hand, and using up the opponents' bidding space on the other.
Say partner opens 2N and you hold S94 H109752 D98632 C5; you can transfer to 3H and actually produce a couple of tricks PLUS an entry or two. Who knows; he might even make it.
But he WILL NOT make 2N.
Or, say you hold S AQ1052 H KJ932 D void C 543
Over 1N, you can transfer to spades, then rebid hearts. Who knows, you MIGHT reach 6H facing SK4 H A1076 D Q106 C AK8
So far we have talked about Jacoby transfers.
Yesterday, I am playing in a pairs game with an old buddy. Put yourself in his shoes. You hold something like;
S 10987532 H void D Q9853 C 6
WE are VUL.
Pardy opens the bidding 1N; 12-14. RHO passes. Do you transfer to spades? (You are NT playing Texas transfers. OLD buddy; remember?)
The opponents have 24-26 HCP. They also are likely to have 9+ hearts and 8+ clubs between them. Even a Texas transfer is fraught with danger. LHO might DOUBLE 4H, and they will reach FIVE or even SIX hearts. Yes. transfers have a downside. Indiscriminate use might facilitate the opponents endeavors. So did YOU find the 4S bid that will silence the opponents?
South African Texas transfers would work well here, but THAT is just lucky. Issues such as protecting tenaces, finding the best "fit" and defining controls are quite subservient to the need to eat up their bidding space. The obvious danger is that your suits break badly and you get nailed for a number. As against that, if you have a 10 card or better spade "fit", THEY may have a slam.
And will they REALLY be able to double you?
Partner bid 2H. LHO finds a horrific double on HK9875. I bid 2S, suggesting 3. RHO now bids 4H on HAQJ642 and some cards in clubs.
Sometimes it is better not to transfer.