According to the United Nations Scientific Committee on the Effects of Atomic Radiation the normal concentration of uranium in soil is 300 μg/kg to 11.7 mg/kg.
It is considered to be more plentiful than antimony, beryllium, cadmium, gold, mercury, silver, or tungsten and is about as abundant as tin, arsenic or molybdenum.[1]
Look around the landscape, if you can see granite then you will have high concentrations of both uranium and breakdown products of uranium such as radon gas in the environment already."Vast areas" is a good thing, it would mean the dense tips of weapons have been broken down and spread out across vast areas thus reducing the concentrations.
It's the high concentrations in small areas that you should worry about.
It should be noted the issue is the toxicity of uranium as an element that's the main cause for concern here .. "depleted uranium" is left over after processing to seperate out the radioactive isotopes for further use within the nuclear industry (weapons, power) and is less radioactive than 'regular' uranium occuring naturally in the environment.
[1] https://en.wikipedia.org/wiki/Uranium_in_the_environment
Rockier regions of EU tend to be on the higher side, almost 3ppm, while lands flatter rolling hills tend to be near or below 2 ppm.
Quoting from table 3:
Lithuania 1.3ppm Russia 1.5ppm Poland 2.1ppm Hungary 2.3ppm
By your logic of solution by dilution we should forget about safely storing highly concentrated waste such as DU and just spread it around evenly through the globe?
DU is a waste product of Uranium mining and fuel production and the industry we've based world peace on, MAD, (since it is the only known model of balance so far). It has no place being used in a conflict zone where it will not only be dispersed from its containment, but be distributed in varying concentration in an uncontrollable unpredictable way. This substance belongs in safe depositories.
Now as far as cigarette butts, my take is that I don't like it, but that is just one slice of a much vaster pie that is plastic pollution. Here environmental damage is caused more by surface area than volume or weight.