This probably doesn't bode well for LinkedIn's Sponsored InMail ad offering.

Over the last week we ran a poll with our LinkedIn audience to get a better sense of what annoys people the most on the platform. And as you can see from the results, 'Unwanted messages' were the fairly clear winner.
This we also ran in our linked in group, which produced a plethora of much more responses but similarly reflected the same result, in terms of messages leading the way.
At over 5k combined responses, that's pretty indicative, and while polls do limit your capacity for context, it does seem you really should be reassessing your usage of blind outreach DMs in the app.

Probably the most annoying uses of DMs, as respondents articulated in the comments, were uninolicited pitches for products, unwanted DMs from the people who want to use LinkedIn to find a date (do not), and people who message you within seconds of connecting, again to sell you something.

Of course, some salespeople no doubt have had success with these efforts, which they'll see as validating such process. But the evidence here suggests that these attempts are generally not popular, and that you'd likely be better off finding other ways to first establish a relationship before the pitch.

How can you do that?

While engaging with user posts, posting in relevant communities, and working to make your presence known to those you're looking to sell to, so it's not just random outreach.

That takes more effort, and time, but if we can glean anything from these surveys, the message is fairly clear that people don't want random invasions in their inbox, even if it is only on LinkedIn.

Getting someone's email address is an act of trust, and it's up to you to make sure that you do not abuse that. It feels less intrusive on the social platforms, compared with getting through to their dedicated email inbox, but the principles are the same. The 'relationship' element is something you should focus on before that hard sell to build a business relationship, or else you might be looked upon as intrusive, inconsiderate, or annoying as a result.