How important is strike when it comes to determining the desirability of a gold coin? In my opinion, probably not as important as it should be and for what is probably an odd reason. For certain series, strike is a critical component in determining the value of a coin. As an example, a certain date in the Mercury Dime or the Standing Liberty Quarter series might be worth $1,000 in MS65 with a normal quality strike but $20,000 with a sharp strike. There are no gold series in which strike carries a significant premium. Why?
I would have to say the answer has to deal with clever marketing. A few decades ago, some clever marketers made up Full Split Band and Full Head designations and proposed that they were worth enormous premiums. It was discovered that these coins were, in many cases, very hard to find with a sharp strike. You could look through roll upon roll of common coins like the 1945 Dime and not find one with Full Split Bands. Clearly the few examples that were well struck were worth premiums.
Why aren’t gold coins marketed with strike designations? Probably because no one has (yet…) thought of a way to make collectors pay a huge premium for a St. Gaudens double eagle with a full torch or a New Orleans quarter eagle with complete feathers on the eagle’s left leg. But if PCGS or NGC were to suddenly bless the concept of strike rarity in certain gold series, you can bet that certain issues would suddenly command huge premiums.
Why should gold coin collectors care about strike? In my opinion, poorly struck gold coins often have bad eye appeal and should be avoided. However, there are exceptions. As an example, certain branch mint issues are always weakly struck. I have never seen an 1856-D quarter eagle that was not very poorly struck and because of this I will not use strike as a consideration when determining whether of not I am going to buy an 1856-D. But an issue like the 1848-D quarter eagle is usually well struck and if I am offered a piece that has a distinctly below average strike, the chances are good that I will pass.
It is important for collectors to learn which issues are well struck and which are not. This is one reason why my books on gold coins go into careful detail on strike for every branch mint issue. If you pass on a lovely original 1849-O eagle just because it has weak stars, you are making a big mistake: every known example is very flat on the stars. But if you are offered a nice Uncirculated 1847-O quarter eagle with an extremely weak reverse, some basic knowledge of the series will show that this issue can be found with reasonably sharp detail on the reverse.
If you decide to collect U.S. gold coins (or any coins for that matter) learning how the coins are supposed to look is any extremely important consideration. Look at as many examples of what you collect as you are able to. Read all you can. The more information you have at your disposal, the more informed your buying decisions will be.