Would a two-seat light fixed-wing aircraft with a landing speed of 20 knots and a top speed of 180 knots be technically possible? Watching helicopters come in to land, on occasion, I have noticed that they approach with a forward speed of a few knots, never land straight down. If there is sufficient landing space, would it be possible in some cases to replace the helicopter with a small fixed wing aircraft with low stalling speed? 

The Helio Courier is an aircraft which is capable of flying slowly:

With a minimum-control speed of around 28 mph, the Courier is perfectly suited for confined off-airport operations. The first one was certified in July 1954 and powered by the 260 hp Lycoming GO-435-C2B2. - Wikipedia

I want to design (on paper at least), a tricycle retractable aircraft which is capable of the 20-200 knot speed range. Why has no one developed such an aircraft, and can the helicopter be replaced in certain situations by such an aircraft? Will it be technically feasible but commercially infeasible?  (Edit: can I do this with increasing wing area and power only?)

EDIT: What I am looking for is an aircraft that can meet these helipad specifications, see page 25 in the document : https://www.faa.gov/airports/resources/advisory_circulars/index.cfm/go/document.current/documentNumber/150_5390-2  and the image titled "Figure 2–7. VFR Heliport Approach/Departure and Transitional Surfaces: General Aviation". 4000 ft approach and 500 ft obstacles outside that. I can fire up my favorite flight sim and try the approach. Stopping within the helipad could be a problem.
At least one airframe close to these specs already exists, its a highly modified Wilga by the name "Draco". It can get off the ground in 120 feet and has a stall speed of ~37mph and cruises at ~180mph. With its epic 4000 ft/min climb rate it can get out of tight spaces fast as well. The only thing it lacks compared to your specs is the retractable gear as it was designed as a big gear bush plane. 



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The same guy (Mike Patey) also built a pretty wild Turbolance experimental that has some epic short field and climb performance as well and its a retract. 

His overall secret sauce is effectively putting a PT-6 on the front end of a small airframe to add a huge amount of power to a light airframe.