So every now and then I have clients who want to purchase a home and are able to pay cash for it. 

Because this is somewhat not the norm, they will often  instruct me to let it be known to a particular seller, "that this would be a cash deal," and that the seller should therefore discount the price of their house by a larger proportion than if the buyer is going through a mortgage company.

There are pros and cons on this issue. Basically, every sale is a "cash deal". After all, the mortgage company is going to be parting with the cash on behalf of the buyer. 

So what are the advantages/disadvantages of a "cash deal" where there is no lender, versus a purchase whereby the purchaser has obtained a loan from a lender?

Well, let's consider the situation wherein the buyer has the funds to pay.

And before I proceed too far on either purchase method, let me mention that in the luxury market, MANY sellers require "Proof of Funds" in the form of a bank statement or an investment account showing immediate liquidity, before they will even allow their houses to be shown.
I recently sold a house in excess of $1.5m. I had to jump though many hoops as the purchaser had a Settlement Statement from their Title Company showing that by a certain date (about two weeks out), that the funds from the sale of their own home, would be available for the purchase of the new one.  Out of about 9 potential houses in that market, four of them refused to show their homes to us as the funds were not "guaranteed".  So they potentially lost out on a sale. What they do not understand is that even with the "guarantee" of the cash in a bank account, that that cash could suddenly disappear from the purchaser's account through many reasons, and the closing would not take place anyway. And remind me to discus the appraisal contingency on a cash deal!

Then there is the buyer who has been qualified by a reputable lender and is in the position to make an offer on a house. Very often the seller will want a copy of the pre qualification letter prior to showing the house. Most listing agents will be more comfortable with the lender's letter than the proof of funds. But then again, that deal may not go through as the lender may uncover a credit issue with the purchaser, or the house may not appraise for the selling price. (there is a remedy for that too)

So what are sellers to do on this issue as to whether to show their homes to "unqualified" buyers, or, demand that all lookers at least have proof of funds or a commitment from a lender? In a perfect world, all lookers would have one of the above. However, as you have noticed, we do not live in a perfect world.
In the end, my advice is that the seller make it as easy and comfortable for any buyer to view the property. After all, one never knows who just won the lottery, and marketing is not a science. 

A further backup is that most agents (Realtors) do not earn a dime if they do not sell a home and it costs not only time and effort to show houses but there is the hard costs of gas, and auto expenses to take into account as well. The IRS thinks that about $0.60 per mile covers auto expenses but in reality, it's a whole lot more than that for Realtors. 

Having said that, most agents will want to know that the buyer is serious, and qualified to buy a house in the very near future. Their livelihood depends on it. A note of caution!! As a seller, I would not entertain an unrepresented buyer.