As mentioned above diversification is really the key since there isn't any chain that will cover every single place you want to visit, or even a majority of them (depending on your travel goals of course). Even if you figured out what chain has a presence in the most countries (which, with some time, I'm sure can be determined), that doesn't help if your chain's presence in a given country is in one city 250 miles from the area you'd like to visit.
The other reasons to diversify are (a) you may not find a reward night available at the time you want to visit with Program A so you need to rely on Program X instead, (b) the available properties in a given program at a particular location may be undesirable for a variety of reasons, and (c) all loyalty programs devalue over time - some worse/more quickly than others.
In fact, personally I've backed off focusing on hotel rewards programs as the value is so poor with most of them anymore. There are better uses for my CC spend than a hotel card (the exception being SPG due to transfers to airline programs). Another exception is a card like that IHG CC since the annual free night cert is worth keeping it - though I don't put much everyday spend on it.