logging: Remove LoggerHandler

[DartBot]

Originally opened as dart-lang/sdk#12031

This issue was originally filed by @seaneagan

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Now that Logger uses Streams (issue #7), what is the purpose of LoggerHandler? AFAIK, typedefs are not exposed for other Streams in common libraries, and shouldn't need to be. Especially if we have some other mechanism to create handlers like issue #11.

[DartBot]

<img src="https://avatars.githubusercontent.com/u/2909286?v=3" align="left" width="48" height="48"hspace="10"> Comment by madsager

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cc @sigmundch. cc @gramster. Added Area-Library, Triaged labels.

[DartBot]

<img src="https://avatars.githubusercontent.com/u/4865287?v=3" align="left" width="48" height="48"hspace="10"> Comment by lrhn

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Added Library-Logging label.

[DartBot]

<img src="https://avatars.githubusercontent.com/u/4865287?v=3" align="left" width="48" height="48"hspace="10"> Comment by lrhn

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Removed Area-Library label. Added Area-Pkg label.

[DartBot]

<img src="https://avatars.githubusercontent.com/u/3276024?v=3" align="left" width="48" height="48"hspace="10"> Comment by anders-sandholm

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Removed Library-Logging label. Added Pkg-Logging label.