Actually we did. In the early 1990s McDonnell-Douglass flew a prototype reusable rocket called Delta Clipper or DC-X demonstrating many of the same technologies that SpaceX is trying to achieve. DC-X in a number of flights successfully demonstrated rocket-borne hover, approach to landing and landing. In one test DC-X landed at its target landing area and then took off again and flew back to its starting point.
However, there is a reason why in 22 years since DC-X's first flight nobody made use of this technology. The reusable first stage does not come for free. The launch vehicle weight at lift off is much higher than it needs to be and the cost of building and operating a reusable launch vehicle are actually higher than that of an expendable one.
First, you need to reserve a lot of fuel for reentry, rocket-borne descent and landing. Second, the structure of the first stage will have to be much heavier than the expendable to take the stress of reentry and landing. It would have to incorporate some kind of landing gear to allow for soft landing.
Third, during a typical launch the main engines run for about 5 to 7 minutes. The reusable stage's engines will run for about 20 minutes. You need larger batteries and more hydraulic fluid to keep them running. Unlike aircraft, rockets use open hydraulic systems where hydraulic fluid is used once and not recycled. The engines of reusable first stage will also have to be capable of deep throttling to allow fine control during the final approach. This adds a great deal of complexity and cost to the engine.
Forth, as I mentioned earlier, a typical expendable engine runs for 5 to 7 minutes during launch. To ensure against failure the engineers design parts of the engine to operate up to 15 minutes. If you plan to run an engine for 15 minutes you have to design the parts to run at least 30 minutes. The only way to do that is make them heavier (and more expensive.) If you want to use the engine multiple times you have to make the parts heavier still.
You can argue that by using some exotic alloys the designers can minimize or even negate the weight penalty, but they could also make even lighter parts for the expendable engine out of the same materials. Anyway, these "exotic alloys" usually cost orders of magnitude more than the more conventional ones, so if you want to use them you incur a cost penalty.
All these things add to the lift off weight of the launch vehicle. Using a wholly expendable launch vehicle you can either use a much smaller and less expensive launch vehicle to lift the same payload or use a similarly sized vehicle to launch a heavier payload.
And finally, if I was a customer, I wouldn't want my satellite riding on top of a reused first stage if it hasn't been thoroughly overhauled and tested after its previous flight. This overhaul would involve a complete tear-down and reassembly the the engines and airframe. The most expensive part of the rocket is the engine. The biggest cost of the engine is the labor to put it together. The same highly paid craftsmen who built the engine will be the ones taking it apart and then putting it back together, completely negating any cost advantage of reusable engine.