The small っ is a pause

The small っ is not a sound of its own. It is a pause as long as an ordinary character: the tongue or lips take position for the next consonant and wait there for a beat. いって is “it-te”, not “ite”. きって, stamp, is “kit-te”. ちょっと, a little, is “chot-to”. The same stop comes before しゃ in いってらっしゃい: “it-te-ras-shai”.

The pause tells words apart. きて, come, and きって, stamp, are two different words — the only difference is the stop. Skip it and you are not saying the same word sloppily, you are saying another word.

っ is a smaller つ, and it is never read “tsu”. See a small つ: pause.