That's interesting. To me looks like almost 100% of the time LinkedIn messages are misdirected and too close to be spam that I almost never bother to reply if I'm not genuinely interested.
When I get a proper email directly to my inbox, it immediately gets my attention and it's likely to get a reply.
99% of the messages and invitations I receive from e-mail and LinkedIn users are by people who want to connect without studying what I do. They don't follow the basics.
BUT, the messages I send try to be laser focused and I have a good success rate of conversions (~20%)
I guess LinkedIn messages are easier for lazy/busy people that need to contact lots of people.
If I get a direct email that is definitely not based on a template means that that person a) found my mail and b) spent some time on the process, so I usually reply as courtesy.
I applaud your approach, although I think it's difficult to get noticed in a noisy channel and LinkedIn messages are overused.
When I get a proper email directly to my inbox, it immediately gets my attention and it's likely to get a reply.