My information is also basically from Wikipedia, so I cannot fully guarantee the following:
Caliph Umar said:
“I wish there was a mountain of fire between us and the Iranians, so that neither they could get to us, nor we to them.”
(A. I. Akram, The Muslim Conquest of Persia)[21]
“I wish that between the Suwad and the Persian hills there were walls which would prevent them from getting to us, and prevent us from getting to them. The fertile Suwad is sufficient for us; and I prefer the safety of the Muslims to the spoils of war.”
(Muhammad Husayn Hayka, Al Farooq, Umar p. 130)[21]
“I wish there was a wall of fire between us and the Romans, so that nor we can cross into their land neither they could in ours”
The Byzantine empire already exhausted after major defeats in Yarmouk and Northern Syria was left vulnerable to Muslims attacks and its very existence in Anatolia was threatened. Umar, apparently was not interested in occupation of Anatolia, it had a cold and mountainous terrain with no economic incentives, soon after the occupation of Byzantine Armenia, the time when chaos was at its peak in Byzantium, Umar had already rejected Khalid and Abu Ubaidah's proposal of invading Anatolia. More over Umar, due to his strong desire to consolidate his rule in the conquered land and owing to his non-offensive policy left the remaining Byzantine empire on its own. The situation was a stalemate, Umar had power but not desire to cross into Byzantine Empire, and Emperor Heraclius had desire but not left powerful enough to roll back his former rich provinces.
(Apparently no reference is given)[26]
Caliph Umar was hesitant to engage Muslims into Egypt to counter Byzantine’s influence there and had to be approved by the Majlis al Shura in Madinah. Umar is reported to have said:
“Life of my one soldier is dearer to me than a million Dirham.”
[26]
Similarly, Caliph Uthman after learning about the miserable conditions of parts of Hind, avoided campaigning in the Sindh interior.
(Tabri vol: 4 page no: 180-181)[27]
If these references are true, then it would appear the Caliphs did not believe it was their responsibility to enforce Shariah on all non-Muslims.
Pakistani scholar Javed Ahmad Ghamdi, although providing a different reasoning than that of self-defence, also claimed in one of his talks that the Muslim caliphs planned to capture only a limited territory and it was not their original intention to move beyond them.
[21].
https://en.wikipedia.org/wiki/Muslim_conquest_of_Persia[26].
https://en.wikipedia.org/wiki/Military_conquests_of_Umar%27s_era[27].
https://en.wikipedia.org/wiki/Military_campaigns_under_Caliph_UthmanAlso read this section,
https://en.wikipedia.org/wiki/Ridda_wars#AftermathAdditionally, from what I know no Muslim armies were sent to Ethiopia or other areas south of the Arabian peninsula even though as these places did not have as strong armies, it would have been much easier to enforce Islam there.
For the related story of Khosrou:
https://en.wikipedia.org/wiki/Khosrow_II#Khosrow_II_in_Islamic_Traditionmore detailed:
http://www.ezsoftech.com/stories/prophet.mohammad1.aspAn interesting account of the Persian chief Hormuzan for repeatedly breaking the peace treaty:
https://en.wikipedia.org/wiki/Muslim_conquest_of_Persia#Raids_of_Persians_in_Mesopotamia_.28638.E2.80.93641.29