If I wasn't eating the meat, I could see the argument for lead, but it's a weak one at best. In my own experience copper bullets do not go all the way through large game. And I don't believe in hunting for purely for sport.
Shotgun rounds are a different thing. Here in Minnesota, they eliminated lead for waterfowl hunting -- which is a fair thing to do. I'll shoot many, many more rounds at birds - and cleaning the shot out can be tricky. Best not to be spraying the land and/or lakes with lead bbs.
Surely you mean copper-jacketed lead, right? I don’t think that solid copper bullets would travel very far or carry much of a punch …
That is very cool to me as a fellow outdoorsman.
Rifle bullets are mostly either lead, which leaves lead residue on the machines parts and causes jams as the tolerances decline. Thus lead coated with copper is superior technology and more reliable but more expensive to boot. It doesn't mushroom as much but the velocities are higher. Plus rifles aren't used around water do they are much less likely to end up in the food supply and this legal for hunting.
Lead Free ammunition exists in various forms and the terminal ballistics can be different than lead ammunition. So many compositions are possible and this is a massive topic that is quite hotly debated and studied in the firearms community.
Most "stopping power" debates are talking about rifles that are vastly capable with or without lead bullets, and with the bans that have happened, the tech has moved forward. e.g. Barnes Bullets (which are copper) are considered a premium round, not just a premium non-lead round. And they aren't really overpriced.
WRT shotguns, I don't know this end as well, but the ammo market could use some forced innovation (the firearms market in general lacks innovation).
Source: https://www.hunter-ed.com/alaska/studyGuide/Two-Major-Differ...
As someone who is subject to the California Safe Handgun Roster[0], the amount of innovation in the handgun space in six years is frustrating.
[0] tl;dr: normal people can't buy a handgun released after 2013 new from an FFL.
As long as lead remains legal to use at the shooting range (where the vast majority of rounds is spent, and most lead is subsequently recovered and reprocessed), it's not a big deal.
I'm not an expert, but a quick Google search suggests that they may be more expensive, less easy to find, and more likely to pass through targets. I found at least one article that claimed they may have greater stopping power since they do not break up in the target as easily. However, I have heard anecdotes about steel shot having less stopping power than lead.