Wood rot tends to be fairly localized. It only occurs in wood that got real wet and stayed that way for a long time.
Also, it's unlikely that the bottoms of the studs are rotten. Wood holds moisture inside it by capillary pressure, and it's unlikely that the studs would have been able to suck enough water out of the bottom plate to start rotting themselves. The bottom plates that were in constant contact with water after a flood would most likely be the only wood to rot.
When you replace those rotten bottom plates, you're still going to need a way to fasten the bottoms of the studs to those new bottom plates, and one option is to use small joist hangers. That way, if there's is any wood rot at bottoms of the studs, the joist hanger will span that gap to allow you to fasten the studs to the bottom plate regardless.
Here are two companies that sell both galvanized steel (which is all you really need) and stainless steel joist hangers for 2X4's online:
Another way to support the wall while the bottom plate is being replaced warrents investigation:
Your can use a stud finder to mark the wall stud locations on the wall, and then attach a 2X4 to the wall using 4 inch deck screws (predrill the holes with an X-tra long drill bit). Now, liberate two scizzor style car jacks from your local auto wreckers for about $1 each and use those to lift up a bit on the 2X4 while the bottom plate is being removed. If the 2X4 is higher up on the wall, just use another piece of 2X4 material on top of the scizzor jack to apply upward pressure on the 2X4.