To quote the description of your link (emphasis mine):
DSECT directive is used to define an area of memory [...] without actually generating any output object code. [...] The most common use [...] is to define the labels [...] that occur in the [...] page zero.
So the reason why you do not get an "A" is that your
DSECT doesn't produce any assembly output at
$1000. However, you could use it to define labels for (uninitialized) variables at
$1000 and following addresses (untested):
VAR1 DS 1 ; byte at $1000
VAR2 DS 2 ; word at $1001
VAR3 DS 1 ; byte at $1003
The advantage is that you don't have to care about absolute addresses. You just list your variables and let the assembler figure it out, and you can insert variables anywhere without having to edit your whole assembly program every time.
And if you are taking over the zero-page, you want to place quite a few of your variables there, so then you use a
(This approach doesn't work if you want to use ROM routines, because ROM zero page on the Apple II is all over the place, so you need to pick them carefully).