Yes, but most people won't "cheap out" on a funeral for their child. You said you don't have kids. Once you have a kid you feel this whole new depth of commitment, protective instinct, and love for them (well, not the sociopath in the story). The death of a child causes a depth of loss that I can't even imagine. Many are paralyzed with sorrow.
Maybe I am naive, but I have a fairly stoic outlook on life. I have no attachment to my own particular death except the fact that I want to be burned and turned to ash after I die. After that, they can toss me in a dumpster for all I care. I just want to be atomically separated and purified by fire after my death, to reduced back to my base components. I'd do the same thing with any child, and simply dump their ashes in the ocean or spread them over a nice meadow. Big funerals are becoming less of a thing now, it's often just private ceremonies and very quiet low key stuff nowadays, I think that's something better to opt for and minimizes the pain of the grieving process.
Cheap would be what I wish for myself. A cardboard casket straight to the crematorium and ashes scattered. But a child's funeral will attract hundreds of mourners, so at the least the family would want a memorial service at a funeral home. That costs. Most parents want a graveside to visit and couldn't bear to cremate.
These are points I find hard to address because my own personal beliefs are biased against burial. The entire process of burial is based upon a literal interpretation of the bible where people are buried in case Jesus returns to rise them from the dead. While I am religious, I do not believe in such a ludicrous and literal interpretation. I think fire is far cleaner. An urn is a suitable replacement for a grave, you can even bury the urn if you want. Perhaps I'm being a bit logical about this, but that would not change my preferences if something real happened.
I had to plan two funerals. Even when you know the deceased didn't want you to spend a lot, it's very hard to stand in a funeral home casket room and say, "I want the cheapest one". The guilt is enormous. Same with flowers. For mom we did buy the cheapest vault (vaults are stupid but required where my dad bought a plot), the next to cheapest coffin, and just two huge bouquets of roses - one for each side. Still, I felt guilty.
Don't feel too bad. I helped pay for a funeral of my fiance's aunt recently, as well as round trip plane tickets, and another plane ticket when I accidentally picked out the wrong date when booking it online, and it goes on and on. And we're still helping pay for it to this day, and I never even met the lady once. These costs can become a burden on the living, and you can rest assured that the dead would not have wanted that. Honestly, they really would not have wanted you to go to huge amounts of trouble. They would want you to remember them, but they would hate for that memory to only be because of debt. So striking a balance is important, and I think you found a decent balance.
When my sis and I were each born my folks bought $5,000 policies (which are now paid off) to cover funeral costs. My husband and I carry lots of insurance to cover that plus enough to pay off the house if one dies before we do that. You and your wife might want to think about that.
Well thank you for giving me these things to consider. I'm only 28, I'm trying to soak up knowledge like a sponge here. Getting married, dealing with lawyers, etc, these are all new responsibilities to me. Reddit is one of the few places where I can actually talk about these things, because death and talk about death is largely omitted from every day conversation.