Most people live in a city where one airline dominates the number of flights and destinations. In turn they tend to frequent that airline and earn miles with them. For me that city is Atlanta and “my airline” is Delta. That doesn’t mean you have to earn every single mile/point with Delta!
You also earn miles and points from credit card spending. In fact that is where I get the majority of my own points and miles! You can diversify by getting a credit card that offers flexible points or miles. You do not have to be chained to a single airline or hotel!
I personally like the new(er) Chase Ultimate Rewards. Every point I earn from spending can be transferred to a nice list of partners both airlines and hotels. The ones worth mentioning are: United, British Airways, and Korean Air for airlines. Hyatt is the best deal for hotel points. The others, in my opinion, are of limited usefulness and not as valuable.
Having miles and points with more than one program gives you flexibility when it comes time to book a trip. If I go to book a trip to Thailand with Delta and find the flights I need are not available I can also check United (Chase transfer partner). I find a flight through United, transfer the points (instantly) and book the ticket. Without the diversity I would have to change my dates or not go.
Transferable points are always your most valuable. Flexibility is the main ingredient to a cheap trip using miles and points. The most valuable transferable points to me are Chase Ultimate Rewards, Starwood Preferred Guest (hotel), and American Express Membership Rewards. I prioritize them in that order.
Keep your options open! Diversify your pool of points to have better chances of getting the trips you want.