The only reason Egyptian Arabic is understood by all Arabs is because all Arab soaps are Egyptian-Arabic spoken. Its known as "oum ad-dounia", the cultural center of teh Arab world. Just like most movies are American-English because they are from hollywood leads to the fact that many non-native English speakers are very familiar with that type of dialect and not Australian, Scottish or Jamaican English for example. Would Egypt have been a small country like Bahrein or Libya and less significant in the Arab their dialect would be less understood because they have distinct pronounciations compared to the original Arabic letters and their pronounciations. The "q" is not pronounced, like "qawi" (strong) becomes "awi", the "j" becomes a "g" like "gadid" instead of "jadid", "th" sounds more like a "s" like "sawra" (instead of thawra/revolution), a "dh" is pronounced as a "z" like "zikr" instead of "dhikr".
It is best to continue learning standard Arabic (fusha) and in your daily life you will get familiar with the daily dialect that is spoken and differs from standard Arabic, although it does have many of its vocabulairy of course. The more you interact with different Arabs the more you get familiar with the different spoken dialects.
Please remember that even in al-Bukhari it is mentioned in ahadith that some Arabs came to the prophet and told him they could not understand (or have difficulties) other Arabs of different tribes. So dialects and differences of it in pronounciation and words used is not something new actually, it was the same in the time of the prophet. Arabia (modern day Arabian peninsula) is huge and because of the desert and tribal bedouin life many tribes lived isolated from other tribes. Northern Arabian tribes were totally isolated from Souther Yemeni tribes, with each speaking Arabic but naturally very different dialects, pronounciation of words and words used. Thats why one standard Arabic was eventually created and is the official language used in all Arab countries and their media for example".
