If the girl is not receiving that many dates, there is more chance that she will appreciate you & wish to marry you, than a girl who has already got her eyes on the next guy lined up for her.
Furthermore, both a girl & a boy, at the end of the day, only need 1 Shidduch:- Period!!
As for the overworked Shadchonim:- So go on a Jewish Dating website, & do your own research & Hishtadlus. These websites are doing a very wonderful service to the Jewish Community, and B’H producing many wonderful & Happy marriages including “& they lived happily ever after” scenarios.
& BTW, nowadays, more & more Shadchonim are also keeping their records on the computer & also networking on websites with other Shadchonim, so what is the difference if you would do the networking instead of the already overworked Shadchan?