The advantage a diamond ring has over anything larger and gaudier is that it's visible, but takes up a small amount of space on a rarely-used digit, and can be worn for long periods of time (Some people NEVER remove their engagement ring, to no ill effect). Other options such as outfits or gaudier, on the other hand, are more cumbersome (Clothes, lol headdresses, broadswords), and/or get in the way (Necklaces LOVE to bounce around and get caught on things during day-to-day activity), and/or need constant replacing (Clothes).
Gold never tarnishes. Diamond is durable and hard-wearing. You never have to replace a ring, unless you remove and lose it. But you never have to remove a ring, so you never have to lose it. A physical, indestructible object is far more permanent than emotions and feelings that can be challenged on a day-to-day basis. Because it's purchased BEFORE the wedding, it's also a nostalgic reminder of when a relationship was enthusiastic, giving a common ground for helping to repair failing relationships. Something that is consumed or temporary(Meals/vehicles), needs maintenance or changes over time (Houses), or becomes indistinguishable from the rest of a person's wealth (Stocks/investments/bullion) doesn't have the same ability to evoke the memories and promises from the beginning of a relationship, and forms a very unstable analogy for the relationship. Houses change over time. Cars are replaced and/or wrecked. Clothes rot away or are shoved away somewhere never to be seen again. Investments are traded and lose their value. Broadswords are just silly. But a diamond-and-gold ring remains as it was when it was first bought forever. And if the relationship does go downhill, you can give the damn thing back. Or keep it as a reminder of how things didn't work out.
And then there's the cost of the ring - One month's wages show that the person is serious about the relationship, especially since most people haven't been working very many months when they get engaged. Talk is cheap, and the flowery romantic can change his mood for a moment in a moment, but the ring says he values you enough that he set aside a significant portion of his earnings to show he wants to spend his life with you. It says he's serious about the relationship in ways no amount of flowery language, no matter how heartfelt at the time, can do. Or it tells you that he's a fool. "One month's wages" instead of some arbitrary, fixed value ensures that the value of the ring is the same for the couple whether they're wealthy or poor - IT IS NOT a competition among women over who has the biggest/shiniest ring - the rings and stones aren't so large and conspicuous that others would notice the size/cut of the gem. That kind of detail is between you and him/her.
Should the diamond stone and metal band itself be negotiable between people? Absolutely, but you need to keep the symbolic qualities in mind and not cast them aside when you change the metal/stone combination - you don't want something that will tarnish, break, or discolor over the next 50-100 years, nor do you want something cheap.