Okay, after reading the OP, explain something to me,
because so far I just don't get it:

That is, from all I can see, the situation in the
OP, admittedly only from an accelerator, is much
like that in essentially all early stage VC firm
equity funding. That is, as in the OP, I'm failing
to see how "both sides of the table" ever have much
chance of shaking hands.

Why? From all I can see, and as mentioned in the
OP, to be considered for any funding at all, even
via an accelerator, the startup needs to have a
product that has traction in the market with that
traction growing.

Before that traction, the guys with the checkbooks
are not interested. With that traction, like the
guys in the OP, I wonder why the heck the founders
would want to take the term sheet, deal details,
check, Delaware C Corp., Board of Directors, etc.
instead of just growing, as in the OP,
"organically".

Sure, I can imagine some exceptions, but the OP
company was just two guys. Moreover, in the
currently running Stanford course by Sam Altman and
YC, the strong advice is to have 2-3 founders for a
long time and be very slow to add anyone else.

So, the OP company had two founders, traction
significant and growing, and, thus, qualified for
some funding but with so few founders likely had
expenses only at the Ramem noodle level and had some
revenue and maybe free cash flow.

So, why take an equity check and all that comes with
it instead of just continuing to grow organically?

Or, net, in simplest terms, it appears that by the
time a startup, based on information technology and
software where the product exists and has traction
and was developed by a team of just 2-3, qualifies
for funding, it will rarely still need or even want
it.

So, I'm losing just where the guys with the
checkbooks expect to find startups they want to fund
that will take the funding.

Yes, I can think of some exceptions, but otherwise,
again, I'm not getting it on how anyone could
expect the two sides of the table to do a deal?

Two more points:

First, all across the US, Atlantic to Pacific,
border to border, in crossroads, villages, up to the
largest cities, the US is just awash in successful
small businesses with 1-3 founders, often just 1,
who do well. Indeed, from all I've seen, most of
the nicer houses, 50 foot yachts, full tuition
checks at private schools and colleges, late model
luxury cars, etc. are paid for by such small
business people.

These successful small business people rarely went
to business school, never watched lectures on
business such as the current YC course at Stanford,
never went to an accelerator, and never got VC
funding.

For being an information technology startup with a
product just software and written by just 1-3
founders and with revenue, that should be one heck
of an advantage compared with nearly all the rest of
these millions of successful small businesses. If
those millions of US small businesses can get to a
good life style business, then the founders of a
good information technology startup should be able
to, also. And for further growth, a successful
information technology startup should be able to
generate plenty of free cash flow -- some software
on a server can run by itself and make money sending
ads 24 x 7 but for a guy with a successful pizza
shop, or 10 such, each pizza has to be made by hand.

Then, with that nice start as a lifestyle business,
maybe that information technology startup could
continue rapid growth to be a major company.

I know; I know; there is a PG essay that a startup
is intended for explosive growth and, thus, needs
equity funding. Okay, but I'm missing just why the
founders won't be happy with $20 million or $200
million and, instead, want to take on a lot of
financial risk and burdens shooting for $2 billion
to $20 billion. A rich guy can easily say, "I
wouldn't walk across a street for another $1
million.".

But in all of this, I'm missing just where the
accelerators or early stage VCs have a meaningful
role to play. The VCs look like the Drawback on a
football team, a third person twiddling their thumbs
in a two person canoe, a fifth wheel on a wagon,
mammary glands on a boar hog, or someone who wants
to buy a ticket on an airplane after it has already
left the ground.

Second, I have to be reminded of the Mother Goose
story The Little Red Hen who found some grains of
wheat but discovered that no one wanted to help her
until she already had on her own built a bakery and
had hot, fragrant loaves of bread and a line of
eager customers and didn't need any help.