Uploading pre-encoded MP4's works just fine. I suggest you download the latest version of the Azure Media Explorer tool for the v3 API. In there you can now upload an MP4 into a new asset, and have it generate the client and server manifests needed for streaming. Just upload to a new empty Asset, and then double click on the asset to get to the tab for the files, and click the generate manifests buttons.
That pre-gens the required manifest files needed for streaming an MP4 that is pre-encoded with closed 2 second GOPs. The tool pre-generates both the client and server manifest and saves them back into the asset to improve the playback performance from the streaming server.
You can use Azure Media Player to play back DASH, Smooth, or HLS - but the technology that it chooses to use for playback differs by platform. For example depending on the browser version, OS, or mobile client it will chose to load a different player tech or it will use the built-in OS player support.
https://docs.microsoft.com/en-us/azure/media-services/azure-media-player/azure-media-player-overview
For DASH content (.mpd) the AMP player chooses to use Dash on Windows, and on Android in specific conditions. It does this by detecting the platform and using the right tech combined with the /manifest(format=mpd-time-cmaf) format on the URL. You can learn more about how "dynamic packaging" works in AMS here - https://docs.microsoft.com/en-us/azure/media-services/latest/dynamic-packaging-overview
There are various "format" options on the streaming locator URL in AMS that provide different manifest formats back.
Smooth Streaming = /manifest
MPEG-DASH-CMAF = /manifest(format=mpd-time-cmaf)
HLS with CMAF = manifest(format=m3u8-cmaf)
HLS v3 (TS) = /manifest(format=m3u8-aapl-v3)
Using one of those various formats, you can use any 3rd party player that supports them. Shaka, HLS.js, Exoplayer on Android, iOS AvFoundation native player, Video.js, or even the 'adpater-player' noted by Jason above. Any player that supports the current HLS or DASH specifications should work.