Why did Jews in the Diaspora have to develop new forms of worship such as synagogue services?

Answer 1

They did not. Jews always worshiped in synagogues, even when the Holy Temple stood. Even within the Temple premises, there were several synagogues. During the Second Temple era, ancient Greek authors attest to the large synagogues that stood in all the countries where Jews lived. The Dioploston in Alexandria, for example, was famous for its size (Talmud, Tosefta Sukkah 4:6). In First Temple times also, synagogues served the same function (of daily prayer and study) that they do today (Talmud, Megillah 26b and Berakhot 31a).

The following changes took place after the Destruction:

1) After the Destruction, sacrifices would not be possible. Prayer (which had always existed) would now be the sole offering to God, alongside the Torah-study and performance of mitzvot (Torah-commands), which had also always existed.

2) In addition, there are a number of commands (relating to the sacrifices, the Temple, and the Kohanim) that we would be unable to perform.

3) Also, the Sages took several steps after the Destruction: they recorded the Temple-procedures in Talmud tractates such as Yoma, Midot, Shekalim and Tamid, and they enacted observances to remember the Temple (Talmud, Sukkah 41a) and mourn its destruction (Talmud, Sotah 49a).

4) The Jewish population was dispersing gradually more and more, so the sages soon permitted the writing of the entire Oral Tradition so it wouldn't be forgotten.

5) Certain changes were made in the daily prayers. Instead of praying that God accept the sacrifices, the prayers now asked for the rebuilding of the Temple.

Answer 2

The Question is based upon a common misconception. Jews always worshiped in synagogues, even when the Holy Temple stood. Even within the Temple premises, there were several synagogues. During the Second Temple era, ancient Greek authors attest to the large synagogues that stood in all the countries where Jews lived. The Dioploston in Alexandria, for example, was famous for its size (Talmud, Tosefta Sukkah 4:6). In First Temple times also, synagogues served the same function (of daily prayer and study) that they do today (Talmud, Megillah 26b and Berakhot 31a).
The following changes took place after the Destruction:
1) After the Destruction, sacrifices would not be possible. Prayer (which had always existed) would now be the sole offering to God, alongside the Torah-study and performance of mitzvot (Torah-commands), which had also always existed.
2) In addition, there are a number of commands (relating to the sacrifices, the Temple, and the Kohanim) that we would be unable to perform.
3) Also, the Sages took several steps after the Destruction: they recorded the Temple-procedures in Talmud tractates such as Yoma, Midot, Shekalim and Tamid, and they enacted observances to remember the Temple (Talmud, Sukkah 41a) and mourn its destruction (Talmud, Sotah 49a).
4) The Jewish population was dispersing gradually more and more, so the sages soon permitted the writing of the entire Oral Tradition so it wouldn't be forgotten.
5) Certain changes were made in the daily prayers. Instead of praying that God accept the sacrifices, the prayers now asked for the rebuilding of the Temple.