Yes the Welcome amenity alone like the cheap $10 wine(which I won't drink anyway)/fruit/chocolate is not worth my effort. But the Welcome Drinks vouchers are different as we usually dine at the hotel restaurant and the additional two Welcome Drinks vouchers are worth $25 off our dinner bill so to me it's worth my effort to chase.Ok... and you think going through all that pain to claim such a bonus is worth the effort??
In my experience, most of the time they would reluctantly issue me the two additional Welcome Drinks vouchers at the point when I had explained the bookings were under different names so not a single stay. I had only needed to "threaten" the check out then check in trick two or three times in my life, and I never had to actually carry out this "threat" in order to get the additional two Welcome Drinks vouchers. So the effort is relatively minimal for me so far(touch wood). I just hate being short-changed and my interpretation of the definition of a "stay" is consecutive nights under the same name whereas consecutive nights booked under different names(no matter whether the two guests are related or not) should be considered two stays instead of one single stay.
But I totally agree with dairyfloss' perfect suggestion of linking the two nights being the most convenient, provided that the guests don't care about the two additional drinks vouchers unlike me. As dairyfloss said, each to their own