From that man page (or my local copy of it, anyway, which at a brief
comparison seems to be the same text as what's at that URL):
>> If no args are present and if the standard input of the shell is
>> connected to a terminal (or if the -i flag is set), and the -c
>> option is not present, the shell is considered an interactive
>> shell. An interactive shell generally prompts before each command
>> and handles programming and command errors differently (as
>> described below).
This states that '-i' makes it an interactive shell.
>> When first starting, the shell inspects argument 0, and if it
>> begins with a dash ‘-’, the shell is also considered a login shell.
>> This is normally done automatically by the system when the user
>> first logs in. A login shell first reads commands from the files
>> /etc/profile and .profile if they exist.
This states that if the shell is also a login shell, .profile is loaded.
From later in that same man page, we have:
>> -i interactive Force the shell to behave interactively.
>>
>> -l Make dash act as if it had been invoked as a
>> login shell.
This indicates that '-i' produces an interactive shell, and '-l'
produces a login shell.
As far as I can tell, this documentation seems to match the behavior you
describe as what you see.
What is it about the man page which you are reading as suggesting that
'-i' will result in $HOME/.profile being read?
--
The Wanderer
The reasonable man adapts himself to the world; the unreasonable one
persists in trying to adapt the world to himself. Therefore all
progress depends on the unreasonable man. -- George Bernard Shaw