Sour water strippers can be rather challenging units to keep operating, depending on your feed quality. Dissolved solids, heavy hydrocarbon contamination, and other issues can foul towers and exchangers occasionally causing out of cycle shutdowns to address the fouling issues. A nice big storage tank can provide you some surge capacity to avoid sour water curtailment in upstream units during an (some say inevitable) outage. Three day storage is a design point I've heard suggested.
As you suggest, a feed tank will also give you a polishing level of feed stabilization. Plenty of skim points and a design to avoid short circuiting are a must. A good tank will help to break some emulsions that may be too tight for upstream separators and protect downstream units from upsets. Again, just a rule of thumb I've heard is 24 hours of residence time with the tank operated at 60% level.
If the downstream acid gas handling unit is a Claus plant, then a storage tank can give you something of a capacity play if the Claus plant capacity is ever limiting. Building sour water in the tank to runback later can provide Claus plant peak shaving capability.
Ultimately, your sour water source and potential comtaminants should play into your feed tank decision. Is this water from a wellhead facility, gas plant, refinery etc? What do you expect in the water that may foul a tower when you boil it and strip it? How much extra capacity is built into your stripper? How expensive is an outage?
This link covers some of the basics of sour water handling if you're interested.
Good luck,
Jason