Here are some speculations why I would think Judaism would never execute [rightfully] convicted Jews right away:
We don't like killing people (even those who deserve it) and try everything within our power to avoid doing so.
We should follow the Pasuk (Yechezkel 33,11) that very clearly shows that G-d prefers Teshuvah over death:
"אֱמֹר אֲלֵיהֶם חַי אָנִי נְאֻם ה"א אִם אֶחְפֹּץ בְּמוֹת הָרָשָׁע כִּי אִם בְּשׁוּב רָשָׁע מִדַּרְכּוֹ וְחָיָה.
שׁוּבוּ שׁוּבוּ מִדַּרְכֵיכֶם הָרָעִים וְלָמָּה תָמוּתוּ בֵּית יִשְׂרָאֵל"
We cry at a funeral realizing that an hour of Mitzvos is worth more than the whole afterlife (Pirke Avot). Why not allow the convict to enjoy some more Mitzvos?
Beruria, R" Meir's wife is famous for changing his mind from killing some sinners and making them do Teshuva instead (Berachot 10a), based on another Posuk (Tehilim 104,35):
"יִתַּמּוּ חַטָּאִים מִן הָאָרֶץ וּרְשָׁעִים עוֹד אֵינָם"
Translation - "G-d wants the sins to be extermined not the sinners".
It appears that killing has no social value, (probably besides "יראו ויראו"), the opposite is true - it is a huge loss to the family, kids, relatives, community etc.
Why is the necessity to execute the convict immediately (Rambam Sanhedrin 13.1)?