As counter-intuitive as it sounds radar contact isn't required to
issue an initial vector.

The words "initial vector" do not appear in FAAO 7110.65, so the only
reason that you say radar isn't required for an initial vector is that
you're interpreting "heading" to mean vector. That is not supported
by the .65. The section you cited, 5-8-2 contains the following:

-----------snip-----------------
5-8-2 Initial Heading
Before departure, assign the initial heading to be flown if a
departing aircraft is to be vectored immediately after takeoff.
-----------snip-----------------

Why isn't this section entitled "Initial Vector" ? My answer:
because it isn't a vector.

Please refer to the definition of a vector in the Pilot-Controller
Glossary.

The definition is ambiguous. It could just as easily be used to prove
my point as yours.

he is restricted in the specific headings he may issue or areas
where he may vector.

Where confusion can arise is when a tower issues a heading that he
intends to take effect once the pilot completes the DP. The pilot can
may confuse this heading for a vector, and circumvent the DP,
anticipating that radar vectors will keep him out of trouble.

I suspect this is why the .65 is *careful* to avoid the use of the
word "vector" with this initial heading. I thnk controllers are the
one who have become sloppy with the terminology.

Now, you may feel inclined to assert that a guy who does the same job
every day for 30 years is far better qualified to know what his job is
than an outsider. Unfortunately, I haven't found that to be true
*necessarily*. I've already struggled with our local class B over
what "established" means, and I won that one, by going to Oklahoma
City, where I found someone who had a better theoretical understanding
of what a controller was supposed to do than the men in the field did.