I'll attempt to answer both your question and what's in the recent comments:
It was estimated that it took 5-7 days for travelers who made the pilgrimage (aliyah laregel) from the furthest places to return home. Thus, the week after the end of Succot is considered a semi holiday.
Why is Tishrei different than Nissan when there is no Tachanun the whole month? I surmise that Tachanun is said during Aseret Y'mei Teshuva already. Since this is a period when you are confessing your sins and are asking for G-d's mercy and forgiveness, it is a time you'd WANT to say Tachanun. So, no matter how you view things, you're saying Tachnaun during some part of the month, anyway. Perhaps, that's what went into the thinking of those that restart Tachanun on Tishrei 24 (Tishrei 25 in years such as this year.)
Of course, based on what I mentioned the question should be "reversed" - Why is Nissan different than Tishrei? I understand cancelling Tachanun after Pesach, but why before it?