This is a neat picture because it shatters that traditional prejudice between Gelug and Nyingma Lamas that's prevalent since the time of the Great Fifth Dalai Lama that culminated with rumors of Kyabje Pabongka Rinpoche smashing Guru Rinpoche statues and chastising Nyingma doctrine. Whatever it was, it has been systematically being put to rest by the current Dalai Lama.
Anyway, with regards to the merger of 4 lineages, I doubt that would be possible as each lineage is different and has its unique qualities and teachings. If you combine all those teachings, it would be confusing to a lot of practitioners. Hence, most ordinary practitioners are not encourage to go around seeking teachings from different Gurus because each will have his own style and method of teaching. Now, if you combine all 4 schools, you are just asking for trouble and I really doubt that the Dalai Lama is even heading in that direction. I believe he is just promoting understanding and peace between the traditions.
On the combination, the Rime movement actually fused the Nyingma and Kagyu schools together, yet it retains the unique points of both schools, which is Mahamudra and Dzogchen. Now, the lineage and teachings of both schools are interchangeable in all aspects. This did not really happen before the Rime movement, if you check with history but it only happened after. The Rime movement did not affect Gelug because Gelug itself was already a Rime movement, so there is no need to re-invent the wheel. While Rime was a fusion of different traditions, Gelug was about taking the blocks from the different traditions, and rearrange them in a way where it can accelerate the practitioner's spiritual progress if followed. The other unique point about Gelug is, it is the only school that places a huge emphasis in the study of logic and the usage of logic in attaining realizations. Dzogchen and Mahamudra traditionally emphasizes more on experience rather than logic or study but Gelug uses a logical approach to it. In other words, it is a complete system by itself so there is no need to tamper with it.
If it is possible to combine 2 schools using Rime, and allow the cordial integration of a third one with the same movement, why is it not possible to use the exact same method to combine all schools? The Dalai Lama has also expressed a very strong wish in the past to fuse all the schools together to encourage unity and therefore, it is not surprising or impossible at all for all 4 schools to merge one day while retaining their unique aspects, and the Dalai Lama implementing a tier system to control them. The Nyingmas did not have a head of their lineage or a representative before the communist invasion, and it was all very decentralized during that period with no hierarchy, yogis and yoginis just band together in small communities or just studied on their own with their Gurus, and they only started it after the Dalai Lama's insistence which they did comply with. If HHDL can influence the Nyingmas, he can influence the other traditions to fuse as well, over time. So I am not that surprised at all.
