The cue bid as a limit raise

I would like to invite comment and in particular disagreement with the following:

The cue bid as a limit raise

I have a friend who contends that on this auction:

1D -(P) - 1H - (1S)

2S

The 2S call should always be a limit raise. I contend that when a support double is available the cue bid is seldom a limit raise. Perhaps that is because quoting Steve Robinson:

“a support double or redouble … shows an unlimited hand with three card support.” So a big hand with three hearts begins with a support double and not a cue bid.

It follows that a direct raise shows 4 card support in the 11-14 range.

A jump in hearts is invitational

4H

With splinter bids available for unbalanced hands.

1C - (P) - 1H - (1S)

4D = splinter in D

Therefore on the given auction:

1D - (P) - 1H - (1S)

2S

The 2S cue bid will, unless followed by a bid in hearts, almost never (I avoid saying never at bridge) show heart support and when it does it will be a game going hand with the spade Ace.