In 34:19 why did the People of Saba' prayed to God to lengthen the distance between their journeys?
This verse shows how the tribes or people of Saba' (distinguish them from the Sabeans which in the qur'an are considered as monotheists) were misguided and didn't have enough faith to thank Allah for His gifts: They were apparently able to travel from Yemen to Syria (Shaam) on a clear road where one "rest station" (visible villages) followed the other. But instead of thanking Allah for this gift they wanted to travel similarly to (all or) many other people who needed to carry their provision with them due to the unexpected and unclear lengths of their journeys when travelling for trading. Which actually was a hardship Allah lifted from them in first place.
Ibn 'Ashur (see here in at-Tahrir wa at-Tanwir in Arabic) tends to the view that this du'a came after a certain revelation, so they might have had some prophets () that informed them, preached and asked them to return to Allah and leave polytheism and shirk, but they rejected and ignored these advises and preaches and challenged Allah by saying something similar to what Quraish said:
And [remember] when they said, "O Allah , if this should be the truth from You, then rain down upon us stones from the sky or bring us a painful punishment." (8:32)
and where later punished and these gifts where taken from them.
You may read abou them in tafsir ibn Kathir (Source):
The Trade of Saba' and Their Destruction
Allah tells us about the blessings which the people of Saba' enjoyed, and the luxuries and plentiful provision which was theirs in their land, with its secure dwellings and towns which were joined to one another, with many trees, crops and fruits. When they traveled, they had no need to carry provisions or water with them; wherever they stopped, they would find water and fruits, so they could take their noontime rest in one town, and stay overnight in another, according to their needs on their journey. Allah says:
(And We placed, between them and the towns which We had blessed,)
Mujahid, Al-Hasan, Sa'id bin Jubayr and Malik, who narrated it from Zayd bin Aslam, and Qatadah, Ad-Dahhak, As-Suddi, Ibn Zayd and others -- all said that this means the towns of Syria. It means they used to travel from Yemen to Syria via towns easy to be seen and connected to one another. Al-'Awfi reported that Ibn 'Abbas said, "`The towns which We had blessed by putting Jerusalem among them."
towns easy to be seen, meaning, clear and visible, known to travelers, so they could take their noontime rest in one town and stay overnight in another. Alla0h says: (and We made the stages (of journey) between them easy)
meaning, `We made it in a way that met the needs of the travelers.'
(Travel in them safely both by night and day.)
means, those who travel in them will be safe both by night and by day.
so far he quoted the blessings and gifts of Allah of the earlier verses!
(But they said: "Our Lord! Make the stages between our journey longer," and they wronged themselves;)
They failed to appreciate this blessing, as Ibn 'Abbas, Mujahid, Al-Hasan and others said: "They wanted to travel long distances through empty wilderness where they would need to carry provisions with them and would have to travel through intense heat in a state of fear."
(so We made them as tales (in the land), and We dispersed them all totally.)
means, "We made them something for people to talk about when they converse in the evening, how Allah plotted against them and dispersed them after they had been together living a life of luxury, and they were scattered here and there throughout the land." So, the Arabs say of a people when they are dispersed, "They have been scattered like Saba'," in all directions.