There have been a number of dominant company coins over the last 800 years or so, all privately issued. Most of these however have been maintained as monopolies over certain geographical regions. Some people call them national currencies or fiat. However many other company coins have tried to get in on the game:
The trouble with this market is that a monopoly is tightly maintained by the issuer of the dominant coin in a region. Witness in recent history the takedown of e-gold, Liberty Reserve, and of the Liberty Dollar. While these takedowns were made with allegations of criminality, the truth is very clear: these folks were doing the same thing the dominant currency issuers were doing.
And so things would remain, if not for the pesky little issue of a decentralized coin technology emerging. The difference with a decentralized public coin is that there's nobody to arrest to stop its use. This means that now there are thousands of alternative coins for people to use. The game has changed.
And since the door was opened by bitcoin et al., now - there is at least some room for new company coins. And they have arrived in droves. Ripple, Iota, ZCash (perhaps not an exact example of a company coin but certainly with some characteristics thereof), Stellar, Cardano Ada, and many more companies are issuing coins and promoting their use now that they don't fear the immediate wrath of the fiat issuers. Some of these coins are at least partially public coins.
The public coin purist will of course recommend public and decentralized coins like Bitcoin, Litecoin, Woodcoin, and many others.
However, these company coins - while corruptible in some sense - may provide certain advantages.
Is it possible that in a world in which nobody fears the monopoly issuer will be one dominated by competing company coins? OK, domination is probably far too strong a word here at a time when bitcoin dominance is still over 60% but at the very least we should keep an eye on this phenomenon: the rise of the company coin.
By now you are probably familiar with the latest coins coming out which fork the BTC chain, effectively making an airdrop instead of a premine (or with a premine as well for the case of e.g. Bitcoin Gold). The first that I know of to do this was CLAMS. The biggest one is Bitcoin Cash. What's the deal? Who's doing this and why?
Basically this represents an acceptance of the by now well-known answer to the question of how bitcoin scales: altcoins. Other coins enable all the scaling one could want and much much more. Don't like the fees and congestion? Move to another chain. This solution is simple, cheap, and already works. Altcoins have been around since day one and are the heart of the public coin ecosystem.
This is all well and good but once this was accepted by some of the big BTC holders (these guys got the nickname "nouveaux douche" over in the trollbox) they realized: why not get in on some of this action using our existing keys? If we can build altcoins to take up some of the slack, in which we are already big holders, this is better for us than people jumping to coins that we didn't take stake in. Plus if they fail, we didn't lose anything getting into the game. Win - win, right?
So now you see the motivation behind this kind of coin launch. Of course there are the other potential motivations which exist in any coin launch: to improve some aspect of the technology, and to enrich the founders (usually by way of a premine which is sold as an ICO).
Sadly a lot of coin users get all upset and imagine that coins other than the ones they hold are bad, because you know, fear the other or some childish thing like that. In fact, public coin is public coin. Giving people a chance to make an educated choice is always going to leave us better off.