If you click the "Connect" link in the sidebar suggestions, it just sends an invite and doesn't give you a chance to customize the message.
I tend to avoid connection requests from people I don't know, or the ones that appear to be reaching out only so they can try to message me to buy some product or service immediately after connecting. I would say about 75% of the connection requests I accept get from people with "default" messages are ones where I know who they are (at least generally), and I don't really need them to elaborate on their connection request.
If I get a request from someone where there is no context and it's just a default message I tend to ignore it.
Or the person made the mistake of linking their contacts to LinkedIn and it try's to make everyone your friend.
I can't even see the message people send when I view the request on their mobile app, so I don't know what people ask in their connection request.
I actually do that if I know the person well, because there's really no explanation needed
FLIR Security | 03/18/16 07:43pm
When I receive unsolicited requests I usually just view this persons profile - if I can not determine an existing 'real world' connection - I almost never agree to the LI connection.
Example: recently I got a generic request to connect - and when I looked him up on LI it turns out he is some guy in Australia who happens to work for a distributor of my companies products in that region - so I connected.
Example 2: any requests from ANY manufacturers in China get ignored by default.