Should they live in the shame and horror of this person that they probably attempted to curb at some point.

No. Those relatives that have not enabled or supported a monsters actions are of course completely innocent.
And if they want, they can of course mourn the loss of the ability to ever have a nice conversation with that person again.
But a burial is not like mourning in your bed, crying yourself to sleep. There you can accept that you are sad about the loss, even tough the world is a better place without that person.

A bureal however is a public performance that, as you say, is for the living. Not for the dead. It is not useful for mourning, but a ritual to pay the last respects to the deceased person. Not only for their good side, but also for their evil side. And the bigger the burial, the greater the (implied) respect. This holds true in any western/materialistic society, and was practiced in ancient times, where pyramids were built to honor kings, and a bigger pyramid implied a better king.

Therefore holding a large burial for a horrific person signals to the living that you not only miss that person as a friend, but also support their actions and choices in life.

Ideally: No.

But i live in a materialistic society where status is expressed trough expensive houses/cars/brands and products.
If you buy a expensive gift (for a living person), you show to them that you are willing to go to great lengths to make them happy.

This is the societal norm in (probably) all western countries. And therefore, making a extravagant bureal for a horrific person implies approval for them and their actions.

So if you are not a materialistic person you can give a small burial to a person without disrespecting them, but there will definitely be some people that will then assume that you did not like that person. They will simply assume it without proof, as it is a custom, unless they know that you are a anti-materialistic person.

A burial is a ceremony where the living show their respect to the deceased. The larger/more extravagant the bureal, the greater the (financial) sacrifice, the greater the respect for the person and their actions.

Everyone who thinks Hitler should have received a state burial (whether by the allies or by his supprters) is definitely a nazi.

Only those that understand a problem even have a chance to solve it. Those who refuse to understand a problem (often for comfort) are not helpful at best, but usually actively harmful.

The problem of suffering runs far deeper than “Rich vs Poor”. We are all trapped inside constantly decaying bodies that are barely capable of survival. This constant decay leads to almost constant pain even billionaires can not avoid. And then there is our anxious brain worrying about all sorts of things that might or might not happen. Yes, all of this is more bearable inside a villa than inside a tent, but it is still abhorrent. This does not mean the “Rich vs Poor” struggle is not worth while. It is, because there is tremendous preventable suffering within this struggle. This struggle, however, is just a tiny fraction of the problem that is called the human condition.

To those who seek to understand the problem of suffering, i can recommend this video. It eases you into the horror of being alive.