The Ki-61 itself was a 1940-41 design concept wedded to the DB-601 engine. Unlike the Bf-109 itself or the Italian Mc 202/205 or G-55, the Japanese did not have ready access to improved DB series engines (the 603 or 605) to substantially improve the plane's speed and altitude capabilities. The improvements that were possible (the all-round vision cockpit in the Ki-61III, increased armor protection, or strengthening the wings to perhaps permit the fitting of additional cannon armament) would not have improved performance (and in the case of the cannon and increased protection might have worsened it)
As far as I can tell, the published literature is not unanimous on whether the radial engined Ki-100 was actually an improvement on the Ki-61. Most likely it was about as good, with the advantage that the radial engines were available and more reliable, with apparent disadvantage of a somewhat slower maximum diving speed. Possibly, had the Japanese designed the plane from the outset for increasingly powerful radials rather than the DB-601, there could have been more Ki-61s, they would be more reliable, and they'd have better stretch. Arguably, however, without the German influence that was partially behind the design of the Hein, radial-engined Ki-61s might have had the same flaws as other 1940-41 vintage JAAF designs (weaker armament, complete lack of protection, etc). Considering that Ki-61s did not reach squadrons in large numbers until early 1943, the much superior Ki-84 with its (unreliable) Homare radial was almost ready - the only fully modern fighter fielded by the JAAF.