There's not, and there are several reasons why this list would be bad for Android users:-
Every new app starts at zero downloads. Focusing on the number of downloads alone would keep old apps at the top of the list, even if they've stopped being updated, while making it much harder for new apps to take off. Even among apps that are all as popular as each other, the older one would always be higher in the list.
If a million people downloaded an app but uninstalled it right away, that means it's less likely to be good, not more likely. Using only number of downloads would give you the wrong information.
Free apps get more downloads than paid apps, because there's less risk: if it doesn't do what you want, or it doesn't work, or you just don't like it, you can uninstall it again. There's already a widespread feeling in the industry that only free apps can survive in the market, for this reason. This is what's led to the growth of apps with ads (and no option to pay to remove them), and microtransaction-based games. Making a list based on only downloads would further depress the sales of paid apps, driving the industry towards making more microtransaction-based games and apps.
Google Play already has a big problem with fake downloads, ratings, and reviews. Unscrupulous developers pay (say) $1 a time for a download with a five-star rating. The download might be performed by a user in an affiliate scheme (so he gets paid, or some other reward, for downloading the app) or using devices with malware. It's an arms race between Google finding these scams, and the unscrupulous agencies performing them. The fact that Google keeps the exact method it uses to decide which apps to show secret is its main tool in making the system hard-to-game. Having a list based on downloads alone would make fake-downloads more effective, which in turn makes the list even less useful, and would increase the value to hackers of compromised Android devices and Google accounts.
It seems you've already realised a little about these differences: in one part of your question, you ask about "number of downloads", then about "which apps people are downloading the most" (i.e. recently, not total number of downloads ever), and then later you want to know "which apps are actually used the most". These are all different quantities.
To come up with the right answer to all your questions, you need a number that's based on the number of downloads over time, weighted to take more recent popularity into account more, along with the "bounce rate" (how many users uninstall the app right away or after a single use), and users' ratings, also considering the statistical difference between free and paid apps. On top of this, it needs to discourage people gaming the system by not giving too much weight to any one parameter.
This is exactly what Google Play already does.