You Don't Have to Allow This
In DnD, party balance is an important aspect. Naturally, the goal isn't that everyone is equally good at everything: characters in particular classes or of particular races will have specialized roles or advantages, which other characters cannot achieve. But overall, the goal is that everyone will have certain advantages and disadvantages which balance each other out. Your player is trying to violate this tenant left and right: explicitly trying to make their character the "strongest" one in the party.
An explicit attempt to unbalance the game is something you don't have to put up with. And nothing in the game requires you to do so. There are no explicit rules in the general rulebooks stating that when a character dies, their player gets to make a new character of the same level, or that they get to reroll the Abilities of their characters. In fact, in the Adventurer's League, the rules on character death (page 7) either require you to raise the character from the dead somehow, or to have the player create a new Level 1 character.
If you are not playing in the Adventurer's League, there are a few methods you could use to curtail this.
Restrict to point buy
This would work particularly well if the other players created their characters through point buy. If they didn't you could work out the point buy value of the characters in your game so far, and allow the problem player to create a character with the point buy value of the highest current character. For example, if one of the other characters Ability scores (before racial bonuses) were 15, 15, 15, 15, 10, 8, you could give the problem player 9+9+9+9+2+0=38 points to create their new character, ensuring that they create a character that is balanced with existing characters in the party.
Restrict to previous rolls (or make the next roll final)
You are well within your rights to restrict the problem player to Ability Rolls they've already made. If you are allowed to roll repeatedly, it basically invalidates the point of rolling at all: why would anyone stop at anything less than 18s in their attack stats at level 1 if they could just keep rerolling until that's what they got? You could warn this player that the next time they create a new character, whatever Ability scores they roll will be the ones they have to use for all subsequent characters.
You could explain this as a balance issue, or you could point out what you've told us: that the constant changes of character are difficult to plan around, both tactically and in terms of the story: that you really need to have some sense of where this player's character is headed to plan ahead yourself.
Raise the Dead
You could, through the players' actions or through the actions of NPCs, raise the player's previous character from the dead. Granted, if they committed suicide before, they're likely to do so again. But you could make it clear that their character getting raised is the only way they can return to the game.
Change their minds, or...
This is by far the most difficult plan, but may be the only viable one.
Your problem player is not only trying to create a character that is strong enough to take on any dangers from monsters, but is explicitly trying to make a character that is stronger than the others in the party. They may be helpful to the party's goals, but they are dangerous to its cohesion and atmosphere.
DnD is inherently a social game. There's no need for our characters to all get along: they may compete, and try to get the better of each other, or even become outright antagonistic. But while this is fine between characters (and could even be a great boon to the story), it is not at all fine between players.
You want your players to work together towards a common goal: that goal is fun. If the players start seeing each other as opponents, then you're no longer creating a story, you're managing group/couples therapy. And while that's an admirable goal, it's not what you signed up for.
This player is abusing a system set up to be balanced, in a way that benefits only themselves. This is apparent not only in their out-of-character decisions to make new characters, but in their in-character arguments that they should get more than their share of the treasure to make themselves even stronger. If you can talk them out of this mindset, then I urge you to do so: but it may not be possible, or it may not be worth the trouble.
I'll give you advice that I hope you'll seriously consider passing along to this player: you want to be the strongest one in your group? There's an easy way to do that. Stay home.