Why Expensive Coins Are Sold Without COA Sometimes?

I've never been hung up on COAs. Whole lot easier to fake a COA than the coin.

Based on my observations of Maple Leaf Forever platinum coins on ebay, the sale price is about $3,000 with COA, and $2,000 without COA.

The coin you give example of, the Platinum Maple Leaf Forever, is not only missing the COA, it is missing the box, and the capsule.

This seriously drops the collectible value of the coin and pushes it toward bullion value. Besides question of authenticity without the COA, no capsule means the coin has been handled with possible fingerprints and scratches. As a coin collector, I would not touch this coin. The seller is realizing this fact and is discounting the coin but with no buyers yet.

Other coins with no COAS, that is easily explained because some coin collectors store their coins in albums, display cases, etc. They take their coins out of their cases and over time lose the COA or box.

In general, missing or damaging packaging affects the value of collectibles. Just look at toy collecting. Toys with original boxes are much more valuable than ones without boxes. Some boxes are worth more than the the toy itself, especially older toys from the 60's and 70's and earlier.

That is extreme... Most NCLT trends to bullion value and I bought and sold mostly through shows and LCS and have never seen a premium or discount related to a COA.

There are all sorts of reasons why a coin is permanently separated from its packaging.

A coin might be bought by someone with an attitude of "I collect coins, not pretty boxes". They buy the coin, and throw the box away. They don't care about potential loss of resale value, because they don't plan on ever selling. Such coins will, however, eventually get sold. Or maybe the buyer simply doesn't have the storage space to keep a bunch of empty boxes.

A coin might get sent off to a TPG by a coin flipper, only to be returned with an undesirable grade (or worse, a bodybag). Seller decides to cut losses and sell for scrap.

A coin might get in a fire, flood or some other natural disaster that destroys the packaging but leaves the coin intact (and a platinum coin would survive both flood and fire perfectly fine). Or maybe the packaging was simply left in a sunny coin shop display window for several years and degraded to the point of having negative value. I've just been given some old 1970s proof sets to try to sell on behalf of a charity they were donated to; the previous owner had neglected them and silverfish have literally eaten half of the COAs. No way am I keeping that COA with those coins when I sell them.

A coin might get stolen and the thief destroys the packaging to remove traceability. Whether recovered by the original owner or not, the coin has lost it's packaging either way.

Whether a coin "suffers" from packaging separation depends entirely on the coin in question. Modern RCM coins like the OP's example are probably best kept in the OGP. Most Franklin Mint coins from the 1970s, on the other hand, are only considered valuable if someone removed them from their packaging as soon as they bought them, because the packaging destroyed the coins. RCM packaging back in the 1960s wasn't much better - even over here in Australia, I know that Canadian coins from that time period are often ruined by poor RCM packaging; I've seen it far too often. So there may even be some veteran collectors from the 1960s and 1970s who learned not to trust packaging from the mints, so got into the habit of routinely destroying the packaging in order to protect their coins.

All assumptions or reasons why missing COA or original packaging make sense. However, the problem is, this kind of offers are observed too often in ebay for such an expensive coin. All those accidents should not happen so frequently. For grading, then the coin should be in a slab with a PF grade.

It depends... When you get into a good relationship with a LCS, you can do a better deal. I almost never sell my collection but when I do sell items to a LCS, it is usually for in-store credit where I also get a discount from list on the purchase. If eking that final dollar out of a transaction is the goal, then you need to sell privately and ideally face to face such as at a show where you set up your own table/booth. To be honest ebay is too much of a risk. If you are not in the business of buying and selling and don't have a large volume, one fraudulent transaction from a shady purchaser on an ounce of gold blows any margin you may have over the course of a year. While ebay fraud is not frequent... it is also not uncommon and ebay do not support the seller.

Plus also... it is a good idea to continue to support the LCS... or they will go away. This hobby would be much poorer if there were no LCS around and it is already a tough market.