I've been looking into SQL Server alerts and it looks like I need to enable database mail on the server to be able to send e-mail alerts. The other solution appears to be to send those events to another server which already sends e-mail alerts (for log shipping), but in this case it appears that all alerts will be sent to the 'other' server.
Are there any reasons that I shouldn't enable database mail on the server generating alerts?
What might be the negative implications of sending all those alerts to another server to send e-mails?
In short, what do I need to look out for and which method is suggested?