They have different target audiences. As has been mentioned, IATA codes are meant for the travel business, for bookings and such and because of that, there are a lot of codes that have no place on the operational side. LON for London for example. It covers the metropolitan area, which is totally irrelevant on the operational side of aviation. There are also a lot of small airports that have an ICAO code and need it, but will never need an IATA code.
Playing devil's advocate and going along with your suggestion(s):
- The number of available IATA codes is limited by the three letter format. If you simply want to add a country code to it to create a four letter code, you're limited to 26 options (in our alphabet) while there are eight times as many countries around the globe.
- If you want to standardise on ICAO codes, you would need to add several to cover the various metropolitan areas that have their own IATA code, such as LON, but they wouldn't be as intuitive as they are today. Whether there's room in the system for all these extra codes... I don't know. The chance of that being the case is better than adding lots of small airports to the IATA codes list. I reckon that ICAO will have something to say about it though as it would add a bit of confusion to several of their systems.