Buying Real Estate through a Realtor - Buyer agent or Seller agent?

My wife and I have debated the merits of using a Sellers agent or a Buyers agent when making an offer through a Realtor. The sellers agent is financially obligated to put the best interests of the seller at the top of their priorities. The buyers agent, on the other hand, has no obligation to the seller and can negotiate without any conflicts of interest.

My wife's main point has been that the seller's agent can help reduce the price. Since the sellers agent will get the whole commission (typically 6% here) maybe they will be flexible and reduce their commission to 3% and help reduce the price.

This is nice in theory but I have found that it does not work out often in real life. Most sellers agents that I have tried to buy through are so emotionally attached to their sellers situation that they cannot focus on doing the deal. I had a back and forth discussion with a sellers agent just this past week who claimed she was negotiable on her commission. The house was owned by a woman who was in a nursing home and needed the money desperately to pay for her care. She had accepted another offer previously, let the buyers move in before closing and when their financing had fallen through, had to evict them, costing her months of time. Here is the Realtor's last email to me:

I am not going to write this up because she will not accept it - and
the deposit is too low- so why waste time? I do not want to waste
ANYONE's time.... my client's, yours, etc... she
can get more for it, she got 3 offers before and sold it for near list
price- you are asking for $30K less just on the list price! That is
insulting.... your 2 week closing is not an issue- the loss of $30K
just in proceeds not to mention the closing costs she has to pay does not
justify your reasoning of a 2 week closing and why she would take it....
that is a huge loss for her.... like I said, she is flexible but she will not
give the house away-

Also the title work is done so her next offer
with a mortgage would go faster than 60 days....

I will ask her
verbally- if you want to waste another agent's time go ahead- I think you will
be hard pressed to find an agent to even do this for you.....I would advise her
not to take it..... if you are not negiotable, why do you expect her
to be?

Now she never bothered to write up an offer and present it to the buyer.(How did she know it was insulting?) I was never able to negotiate with the buyer (how did she even know if I was flexible?) How did she know another closing would be fast? (Bank paperwork is usually the holdup here - not Title work - I can close in 2 weeks with my Hard Money lender)

So, I called my Buyers agent and she wrote up the offer within an hour and I submitted it. I doubt the Realtor even bothered to show it to her client. She let her ego overcome any sense of professionalism she might have had. This is not the first time this has happened to me with a sellers agent. Many have the same sense of defensiveness about their clients. This doesn't really serve the client well, despite how it seems. An agents job should be to impartially submit an offer in my opinion.

I think the possibility of saving a few dollars using a Sellers agent probably cost me even the chance of having someone look at my offer. For every deal that might save my a few dollars using a sellers agent, I probably will lose tens of thousands of dollars in potential profit through lost deals. I won't make that mistake again.