As stated by seldom, there was a previous string devoted to this topic. I do however believe, if my mind serves me well, that it was devoted more to structural steel work although the answers did discuss the issues in piping as well.
I can only say that if propper care is taken, there is no reason why welds can not be very close together. (T joints are two welds that run right into each other!) I believe that in ASME VIII there is a 50mm (2") limit to the spacing of welds. (Also based on the material thickness.) This will sometimes be contravened due to practical reasons.
You mentioned that you understand the metallurgical reasons for not getting the welds close together. Well, it depends on many factors but metallurgically speaking it can be beneficial for welds to be very close together as the second weld will tend to refine the first weld. For this to happen however, the welds need to be VERY close together. A typical HAZ is anything from 1 - 5mm deep depending on the welding parameters. You can therefore see that in most cases the spacing limitations has very little to do with the metallurgy of the weld. It is rather a matter of workmanship due to the distortion surrounding welds and possible residual stresses interacting with each other.
Hope this helps.
Regards
Niekie Jooste