If we take a look at Xanathar's Guide to Everything (201), we can see that they offer some suggestions for magic items, which we can then compare to the amount of gold our players receive. A common magic item averages only 40 gp, uncommon ~300 gp, rare ~11,000 gp, very rare ~30,000 gp, and legendary ~175,000 gp. So right from the start, we can see that if a player saves and saves every copper they could expect to get in a level 1-20 campaign, they won't be able to afford the legendary item until they receive one or two rolls for treasure level 17 or higher. Once your players enter Level 2, they will have their favorite team and gold will start to lose meaning to many of the players because it doesn't really matter how much gold they have.
They start with their tier 1 gold according to their class, and then add the next gold based on their initial level. One option to determine your starting gold is to get a gold fund and use it to buy your initial equipment. There is nothing intrinsically wrong with random tables, but I note that it only takes at least 10 gold a day to live like an Aristocrat, and you can throw all the gold you want at it. The new character will have enough gold to buy competitive equipment, but will not dominate the other characters because gold can be spent to fit the setup perfectly.
A character who retires at level 20 and has the average amount of gold and artwork thrown for him should retire with a total of 786,086 gold pieces.