I used the "shotgun" approach for the first time just this past weekend and it worked quite well for me.
The context: big city, very narrow window of time for daytime appointment, holiday weekend, me hosting in my hotel. Sent the exact same message to a half dozen new-to-me gents about 24-36 hours before the requested appointment. Four replied in a timely manner to let me know they weren't available in my admittedly quite narrow timeframe; one replied to confirm he was available and interested; and one never responded.
I booked with the one who replied, for a very gratifying encounter. Enjoyed brief, clarifying, and very friendly exchanges with two of those who replied, bumping each of them to the top of my priority-hire list.
For me, it was an effective use of the approach. Not a strategy that I would use in most situations, as I prefer to hire with a longer lead time, which typically allows for one query at a time. But, under these circumstances, "the shotgun" style was quite effective, in both the immediate and longer term...