[shevek]

We had this success yesterday

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Pleasing that the ♣K was offside, so 4♠ had no play, while 3NT is heaps better.
We admit that these gains are rare and there is a cost in dreaming about them.

We give them lead-directing doubles, plus help them to lead and defend well, risk wrong-siding.
In the long term, is the effort worth it?

[hrothgar]

I view relay in much the same way that I view strong club openings: A whole bunch of the benefits come from the hands where you DON'T need to relay

I don't tend to worry much about lead directing doubles and the like.
These are going to come up almost regardless of what system you're playing.

You obviously want to be able to right side the contract as often as possible
And you want to be able able to punish the opponents if they chose to make a lead directing double

[helene_t]

Interesting. My first reaction was that it was a bit of a lucky strike, giving the information that South has, but actually it is difficult to construct a North hand with values and length in diamonds for which 4♠ will be better. If North only shows length in diamonds and not values, something like xxxx-Kx-xxxx-Kxx would feed the bill, though.

Maybe the loss on the hands on which you end up in an agricultural 4♠ after a full relay sequence is too big to be compensated by the rare success stories like this one.
But I agree with Richard that your gain is primarily on the hands where you don't use the relays.