Yes, it can be a slog. But the links, when/if you can acquire them, have a pretty good trust profile. Sometimes the outreach conversion rate can be surprising, particularly if your site offers some kind of advantage over the competition, as well as sprinkle some trust signals to inspire confidence in the site and encourage them to believe that a link to your site belongs in their resources section alongside those of your competitors. Trust signals are typically an award that the site received, some positive press mentions, etc.
Put the trust signal ducks in a row prior to starting a link beg campaign, and that includes the broken link gambit. I wouldn't recommend the link beg otherwise.