Describe the new feature:
osu!lazer would show suggestions of downloadable beatmaps inside the beatmap carousel, they would either be half the opacity or have a little cloud icon, clicking on them or pressing enter, would show a progressbar under them and automatically start playing when downloaded. Missing difficulties will be also be shown, unless hidden by the player.
Limitations:
osu! shouldn't show them if the search entered is too broad (over 10-25 results, most likely searching an artist).
The alternative to this would be that osu!lazer only should show the first 5 most popular maps, with an entry linking to osu!direct.
Proposal designs of the feature:
Normal:

Downloading:

I'm quite opposed to this, it feels really intrusive and one step removed from advertising to me. No need to stuff "automated recommendations" anywhere they could go.
In my opinion, it can be optional of course, if the player searches for something they know of (e.g. a popular song), it would be neat if osu! could show existing beatmaps so the player doesn't have to open direct first.
But I do agree that osu! shouldn't recommend maps everywhere, the scope is intended just to be the search inside the song select.
Seems unnecessary IMO because the osu!direct can be opened just by Ctrl+D, I don't see a difficulty with just searching there.
I think an alternative to this would be to possibly have an option to load the osu!direct overlay with the currently inputted local search text. So, when no local entries can be found you can bring up direct with what you were searching for locally. (Hopefully that made sense, and it's not already implemented lol)
@mouzedrift's suggestion was to add something like this

only if no beatmaps were found
Maybe add an entry at the end of all beatmaps which says "Search online for beatmaps", which when clicked brings up the direct overlay searching for the specified name.
EDIT: ninja'd, I am in china so sometime the images won't load
I think we should completely rethink the way beatmap discovery and storage works and get rid of having 2 different places to search maps (direct and songselect) in the first place:
We also do have plans on adding a method of getting from song select to online results via a panel or other display, but this needs design / UX considerations. It would also display in cases the user has no beatmaps loaded, for instance.
I do have an eventual plan to add "cloud storage" of user's beatmap lists (maybe supporter only), which would download on-demand when a beatmap is accessed.
Most helpful comment
We also do have plans on adding a method of getting from song select to online results via a panel or other display, but this needs design / UX considerations. It would also display in cases the user has no beatmaps loaded, for instance.
I do have an eventual plan to add "cloud storage" of user's beatmap lists (maybe supporter only), which would download on-demand when a beatmap is accessed.