Actually, there are three ways to have a kong:claiming 3 kans is the result of 3 explicit kan melds.
1. Melding a pung into a kong as you describe
2. Extending a Melded pung into a kong
and 3. drawing 4 identical tiles, declaring it as a CONCEALED Kong and placing it aside on the table (most japanese rules require one or more tiles to be face up ... though some rules and quite a number of non-japanese rules allow them to be placed on the table face down ... which in my opinion is fairer as declaring a kong puts you at a disadvantage compared to using the same four tiles in two or more sets). The Kong even though concealed is still considered part of your hand. If you got to the point of self drawing these tiles you would consider at least at this point which hand you wished to score it as. If it was with the kongs you would declare them and draw your missing tiles to enable you to complete your hand.
The statement I made above is a incomplete partial hand only waiting on 1 or 4 tiles depending on your choice of ryan-peikou or san kan tsu.
Normally you would have decided that the 3 kongs score more and go for that ...... But if you find you\'re against an early reach and find that you draw the remaining 1,2,3 dot safely discarding you could easily find that you could be in a reach situation with ryan peikou particularly if you have as half your head another dot then you could reach waiting for the remaining dot giving you ryan-peikou & chinitsu.
Again here you are assuming that one would decide to go out on this rather than declare the kongs.1111222233335 : 4p will give you chinitsu only
If you were dealt 1111 2222 333 and drew the final 3 in the first couple of draws you would more likely declare san kan tsu than later. Effectively giving you three extra draws to improve your hand. If you are oya/east and have a east in your hand .... I\'d be tempted to go 3 kans and draw an extra 3 tiles hoping to pull an east from the kong box to end up with san kan tsu & fanpai & hoitsu ... haneman! In a midgame hand where my opponents have melded a few dot sets, I might be tempted as well .... the possibility of ryan peikou + chinitsu not looking good and a few odd tiles of dragons, seart or round winds in hand ... I may consider declaring the concealed kongs and pulling 3 from the kong box hoping to pair off the wind/dragons for ryan peikou + honitsumaybe getting up to mangan (or even a haneman if I am dealer and pair off my wind plus either menzen tsumo or riichi).
Later in the game, say in the midgame, you are almost certain to go the ryan peikou approach and reach with a likely mixed hand.
You have to consider not only what you have in the hand, but how early in the game, discards, opponents melded sets and the overall points situation before you decide on which approach to make.
There is no point going for chinitsu or ryan peikou only if you are behind and need a mangan or haneman to pulll enough points near the end of the match to get through to the next round of a tournament.