The core module File::Fetch solves the problem by trying LWP, HTTP::Tiny, wget, curl, lftp, fetch, HTTP::Lite, lynx & iosock:

perl -MHTTP::Tiny -le'print HTTP::Tiny->new->get("https://perlmonks.or
+g/")->{content}'
[download]

IO::Socket::SSL 1.42 must be installed for https support
Net::SSLeay 1.49 must be installed for https support

perl -MFile::Fetch -le'$f=File::Fetch->new(uri=>"https://perlmonks.org
+/")->fetch(to=>\my$data)or die$f->error;print$data'
[download]

Success!