No you don't miss anything as we have no consensus on the matter until today.
For example this fatwa on islamweb #1126768 clearly rejects using calculation for predicting a moon sighting. And explicitly rejects or refutes the "convention" of the ECFR (European Council for Fatwa and Research) and considers it as an order to do what neither Allah nor his Prophet () ordered us to do if we followed the ruling described in the convention and therefore recommends to rely on local sightings. They also made clear that neither the Qur'an, nor the sunnah nor the consensus supports an astronomical calculation for moon sighting and posted a statement of ibn Tayymiyah which supports the naked eye/real sighting and rejects any calculation. Note that some scholars consider the calculation as an incertitude based "Information/Conclusion" (as it is calculated, but one cannot -always- witness it -think of a cloudy sky-) contrary to the certainty of sighting a hilal by naked eye or a telescope for example. The fatwa also discusses the fact that the unity is only local in Europe while if a Muslim unity is desired, it should be world wide.
Nevertheless there are a few pros in this if it was applied: For example all Muslims would start fasting the same day etc.. Muslim communities in non-Muslim countries may have a basis to ask for their own days of celebration.
There's also a point that might lead to the conclusion that a sighting can be useful in situations, which often apply in winter in Europe and Northern America which is that the sky is overcast and it is even hard to follow the moon phases earlier, so if we had no communication possibilities we may never know which month is elsewhere nor find a good position for a possible "moon observation" as for a good moon sighting one must know where at the sky one must look at the given time or one may observe -in worst case- other celestial bodies (like in this case). Dr. Taha Jabir al-Alwani said in his book Ijtihad (1993, page 27):
”…It could never have been the prophet’s intention to make life so difficult when he established that rule. He was, at that time, addressing illiterate people, and the best they could do to establish the beginning of the month was to see the moon with the naked eye. They had no other means and Allah (SWT) did not wish to make matters difficult or impossible for them. But when there exists more accurate instruments to determine the same fact, it would be totally unacceptable, and indeed backward looking, if insistence is on using out-dated and inadequate methods. The message of Islam is intended for all people in all ages; it was never restricted to the first hijri century Arabs of Makkah. Therefore, to stick to the literal meaning irrespective of the time factor is a benighted approach which is conducive neither to enlightment nor to progress.” (Source moonsighting.com)
Let me give you an example often we have the situation that Saudi Arabia (relies primarily on the Umm al-Qura Calendar -which was often revised-, but tries to back it up with local sighting reports) a sighting is reported while in Morocco (relies on local sighting) not, from the astronomical perspective this can't be correct (nevertheless all independent calculations show that Saudi is wrong the error rate of the Umm al-Qura Calendar is legendary, read for example this article and here). Note that Oman which is situated on the Arabic peninsula and also uses a local sighting usually also disagrees with the Saudis.
So on the first night of Ramadan in Morocco you may observe a well formed crescent moon (we may think it is 2 or even 3 days old), some people therefore may ask themselves "Have we started fasting too late?" due to this observation. Therefore it is possible that some scholars thought in the early ages of Islam people were not able to see the moon if the sky was cloudy, and even later when telescopes have been invented it was not therefore using the aid of computers, modelling methods and strong algorithms might be of use to clear the doubt of what might have been seen if there were no clouds in the sky. Some may say the early Muslims didn't care why should we do so? other may say good idea. Note that similarly to the situation described above in case of a cloudy sky people may experience the same situation of a crescent moon which looks like two or three days old (or generally older than expected).
Finally as an evidence against calculation we may use the sahih hadith:
We are an unlettered people who can neither write nor count. The month is thus, and thus. folding his thumb when he said it the third time.
(See for example in Sahih Muslim, Sahih al-Bukhari and the Sunnan)
A side note a few weeks earlier I've read on www.moonsighting.com that calculation for moon sighting was considered as invalid 100 or maybe even 50 years ago (I'm not sure which number is/was correct in worst case both).
See also this blog post.
