You owe it to yourself and to your work to labor over your query letter. Each element is essential. The query letter is selling yourself as much as it is selling a script. It may not be fair, but it happens. They can presume your script is like your letter, so make sure you're conveying the impression you want.
Many agencies accept the loglines separately on a second page.
All that means is that the first page is shorter and faster to read. Perhaps these things seem obvious to you, but agencies' and prodcos' experience say otherwise. Many writers would rather write three scripts than one query letter, but they really aren't that hard to do well. Maybe you're an introvert and the party analogy is frightening as well. There is no other way.