Since the 800 final had 10 runners in it, I'm going to count up the number of runners in each men's distance race from each country who finished in the top-10. Also going to score it like a track meet (10-9-8-7-6-5-4-3-2-1 scoring), and give the final medal counts as well, so we can see where the US stacks up objectively.
Overall number of athletes in the top-10 should be a good measure of depth, medal count should measure top-end strength, and points earned in scoring should be the best overall measure.
Format is
Country - # of competitors in top 10/score/medals earned
800m
Kenya - 2/11/Silver
South Africa - 1/10/Gold
Bahrain - 1/8/Bronze
Russia - 1/7
Morocco - 1/6
USA - 1/5
Netherlands - 1/4
Poland - 1/3
Cuba - 1/1
1500m
Kenya - 2/13
Bahrain - 2/12/Gold
USA - 2/11/Bronze
Ethiopia - 1/9/Silver
Morocco - 2/6
France - 1/4
Steeple
Kenya - 4/30/Gold/Silver
Ethiopia - 2/11
France - 1/8/Bronze
Finland - 1/3
Spain - 1/2
Bahrain - 1/1
5000m
Ethiopia - 2/15/Gold
USA - 2/12/Silver
Qatar - 1/8/Bronze
Kenya - 2/8
Uganda - 1/7
Great Britain - 1/4
Spain - 1/1
10000m
Ethiopia 3/18/Gold
Kenya - 3/18/Bronze
Eritria - 2/11/Silver
USA - 2/8
Marathon
Kenya - 3/25/Gold/Silver
Ethiopia - 2/15/Bronze
Japan - 1/5
Morocco - 1/4
Portugal 2/3
Spain 1/3
Totals
1 Kenya - 16/108/2 Golds/3 Silvers/1 Bronze
2 Ethiopia - 10/54/2 Golds/1 Silver/1 Bronze
3 USA - 7/36/1 Silver/1 Bronze
4 Bahrain - 4/21/1 Gold/1 Bronze
5 Morocco - 4/16
6 France - 2/12/Bronze
7 Eritria - 2/11/Silver
8 South Africa - 1/10/Gold
9 Qatar - 1/8/Bronze
10 Russia - 1/7
10 Uganda - 1/7
12 Spain - 3/6
13 Japan - 1/5
14 Netherlands - 1/4
14 Great Britain - 1/4
16 Portugal - 2/3
17 Poland - 1/3
17 Finland - 1/3
19 Cuba - 1/1
Analysis
Kenya is the clearly dominant force, with Ethiopia a clear second as well. The only way to justify bumping the US out of it's spot as #3 is to put an extreme amount of weight on the value of Gold medals, which would move Bahrain into third and the US (at worst) to 5th, though I don't think anyone would try to make a serious argument that South Africa, who qualified a total of 8 male distance runners into the entire meet (3 in the marathon) and whose next best finisher was 12th place, is better than the US. Morocco is a curious case, placing 4 in the top-10 but none higher than 5th, with France/Eritria/South Africa/Qatar/Russia/Uganda all not having much depth but all capable of putting out a medal contender. I think the US is a clear #3, Bahrain a clear #4, and I'm a bit hesitant to give #5 to a country whose best runner placed 5th, but Morocco is certainly a top-10 as well.