discount or a freebie? When do you guys think it's appropriate

Whenever she wants.

leaving the client stuck with a hotel room, or just wasted opportunity.

Over the years I had one situation where there was a discount from a previous last minute cancellation and one other situation of free a get together, I guess because of "appreciation".  I didn't ask "why", I just said "yes" lol.  However I confirmed a few times to make sure she really wanted to do this and made sure we were on the same page.  No miscommunication.  Me: "so....I'm going to just show up, nothing in hand.", Her: "Yes"

Naturally the agency only should have the right to waive the agency fee and not ask the lady to work for free unless of course it's her choice as well.

...a little punch card that when the 10th one gets punched it's free ? Like the car wash or barber shop ? I'm liking this idea...

I've had an agency waive their fee one time and several providers have given discounts for Veterans Day etc. so my answer is Maybe... Sure

We establish points and every 1000
Points we get a discount  

I made a date through a very reputable agency with whom I had worked for a year or two.  The woman who ran the agency knew my age (late 60s then).  The date was with a young provider (20ish) and was TERRIBLE.  She simply had a lousy time and it showed; absolutely no connection real or simulated.  After the date I called the agency and politely complained or, perhaps I should say, reported.  The owner immediately apologized.  She said she knew that the girl did not like older men and she should never have allowed me to make the date.  She offered me a free do-over.  On the second try a good time was had by all.

each woman considers each client on an individual basis.   i wouldn't call them discounts, but i know i give a donation specific to me and no other client to more than one provider i see.  there is one lady i have seen for more than 4 years who still asks for her original donation from when we first met, while having raised rates on other gents.  i recently got a really nice break on a dinner date, not only was the lady's requested donation for me lower than her posted rate, we were together for about 2 hours longer than the original contract was made for, and not a peep was said about it by her, tho several moans and a few oh gods yes yes right there yes! were heard.

It should be done for your loyal clients.
I have given some providers gifts in the past and have received extra time too.
So it's all about chemistry between the two parties.

When I see a provider on a regular basis I can usually get a pretty good discount after about a couple of months. .

Foxy Roxy, for regulars I know that providers do give discounts to them all the time to retain their client base.
Also Roxanne, it is commonplace to give discounts during the summertime and other times when it is typically slow to induce business as well.  Complimentary sessions could be on the client's birthday or an occasion if a girl had a reason to cancel unexpectedly.  But it does happen more than you think.

...her friend is available. Maybe a freebie is a bit much, but a discount would be in order.

just mathematically speaking, if a lady asks $600 an hour but lets her client hang for an extra 15-20 minutes, that's like offering services worth $150-200 extra for nada.  kind of like a discount.