Here is parts listing from a Cooper to Cooper S project using secondhand parts (DIY so no labour costs) completed by a member of TotalMINI.com:
(Link to TM site is currently down due to their server problems) totalMINI
6 SPEED GEAR BOX
TWIN EXHAUST SYSTEM
2 DRIVE SHAFTS
EWS IGNITION BARREL & KEY
WATER RADIATOR & FAN
everything brought.. approx £1500
everything sold.. £650
cost to make this Cooper an S.. £850 R53 Cooper S Engine Conversion: The Complete Checklist: R53 Cooper S Engine Conversion: The Complete Checklist
These kind of conversions tend to be done by enthusiasts who enjoy the challenge of building their own unique MINI from parts and can then get a reasonable insurance quote at the end. The high labour costs also mean it is usually only done by experienced DIY home mechanic enthusiasts to be economically viable.
Such engine conversions are of course very common in the classic Mini world as a genuine early Mini Cooper S is now a very rare and expensive classic car...........but as said the modern R53 MINI Cooper S are fairly cheaply and widely available at present, so it makes less sense to do. This may change in future years as the usual attrition rate of performance cars makes the R53 Cooper S a much rarer 'future classic' and harder to find in good condition at a reasonable price.