Earlier quoted context omitted.
For all of the reasons you gave (except search--that's what grep is for), I usually reach for `man`. But, for wget the information density of the man page is just wrong. At least these days it has some more information in it--it used to just be a reformatted version of the --help text, plugged into a generic template.
grep on help output is annoying sometimes since many programs send it on stderr and you need to redirect it if you want to pipe it to grep. Plus even if grep matched something you can't read the context without extra options. man is much easier than doing all that, but the time you have your full search command you would have already gotten your info from man.
For context try grep -2, where 2 is the desired lines of context.
$ wget --help |& grep -2 base
-i, --input-file=FILE download URLs found in local or external FILE
-F, --force-html treat input file as HTML
-B, --base=URL resolves HTML input-file links (-i -F)
relative to URL
--config=FILE specify config file to use
--
existing files (overwriting them)
-c, --continue resume getting a partially-downloaded file
--start-pos=OFFSET start downloading from zero-based position OFFSET
--progress=TYPE select progress gauge type
--show-progress display the progress bar in any verbosity mode
(Not that I'm arguing that this is an excuse for wget's [and GNU projects' in general] man pages sucking, but it's a useful workaround.)