Covers take up a lot of space. Those who collect used stamps may not like to use a lot of album space to house a cover when all they want is the stamp. For very common stamps, covers do not add much value. The limited demand may make them difficult to sell.
For classic stamps, covers may add some value.
First day covers, except for the earlier ones, have very little value. The stamps from those covers have recognisable cancellations that will make them worth less than genuine postally used examples. Some stamps from the UK only exist from FDCs. It would make sense to soak them off those covers to add them to a collection.
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it's okay to do whatever you want, there no right and wrong way
It is. You decide what you want to collect. No one else does.
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It does seem, however, that the cheapest way for me to get the missing sets is to buy collections of old covers. The best solution would be then to cut the group of stamps off the cover and mount the group in my album.
Nothing wrong with that for the above reason. Keep in mind most collectors will consider stamps soaked / cut from FDCs spacefillers. But then, it is not their collection.