First, can I commend safetypee's observations and thoughts - he has a lot of very appropriate runs on the board in this sort of area over many years and his counsel is well worthy of our attention.
My thoughts, as a sideline -
(a) why don’t we use a factor for wet runway on take off The standards for scheduled performance differ significantly between lighties and big iron and it is worthwhile having a read through both Part 23 and 25 (along with the relevant flight test guides) to get a basic overview of the differences. A rather decent read, though, and you can anticipate going through a large jar of coffee in the execution. One needs to note that, should we be talking about a particular aircraft, it is necessary to do some homework to identify which revisions of the design standards might be the most appropriate to review.
Basically, it comes down to using AFM/POH guidance, should it be available, or standard factors, such as safetypee has suggested or, if you have some mathematics in your background, doing some sensibly conservative sums to give yourself a bit of a pad. Blindly launching in blissful ignorance of anything to do with runway contamination probably is not a good idea.
I had a quick look at the DA42NG book from the OEM site and it seems to provide a better than average set of guidance compared to what we might see in many other light aircraft POHs.
(b) In any case the pilot must allow for the condition of the runway to ensure a safe take-off. Be wary of recommendations for surfaces such as grass. The data is based on presumptions as to coefficients of friction (rather than grass lengths, etc., although reasonable if from a respectable source). Please do be both careful and conservative. I note that the OEM has provided both ground and air distance data so we have the basis for some sums to target a go/no go lift off point decision for strips which might be approaching limiting lengths; better to call the reject and hit the fence at low speed rather than continue and hit it at high speed ?
(c) The take-off distance on a paved surface is not influenced to a very great degree by water on the runway That might be a reasonable call, depending on what kit the aircraft may have. I'd rather give myself a bit of fat to keep the excitement level down to a sensibly calm level, suitable for old chaps. If it's wet seal, and I don't have anything else to work with, I'd still want to give myself a pad, even for the continued takeoff case. Just because there might not be a rule saying I should doesn't preclude my doing so.
(d) I suspect that Diamond did not test these situations and therefore will not be able to provide any factors for those situations Refer to (b). The best we can do for grass surfaces is make some calculated guesses as to what might be good coefficients of friction for the sums and then come up with fudge factors based on the sums. Just what you might get for a given surface may be somewhat different to what the OEM opines. There are techniques whereby you can run highspeed taxy tests to get an idea but that is probably not useful for the typical light aircraft pilot. I recall reading a rather old report which looked at this for a single engined military jet.
(e) We don’t because it’s not required for the rules under which we fly and the rules under which the aircraft is certified. Its that simple. As I observed earlier, just because the rules don't require a pilot to think, sometimes, perhaps it might be a good idea anyway ? If it all comes unstuck, you're dead, not the Regulator who decided that a rule wasn't appropriate.
(f) You don’t need to worry about V1, screen heights or second segment climb performance. The POH might not have data if it's not required by the design standards and we all have a handle on why that is so. That doesn't mean, though, that we ought not worry about such things or, at the very least, have a bit of a think about them and inject some conservatism into the operation.