It is obvious that this cycle of songs is conceived as such: it is completely through-composed. Some people even don't recognize that it consists of separate songs. Its strict structure around four motives introduced in the first song is very characteristic for Beethoven.
With respect to the metric structure of the cycle (3/4-6/8-4/4-4/4-2/4-2/4;3/4), there is not much logic to find, except for the fact that the cycle starts and ends with a 3/4 and everything in between has a structure with a metric accent half way the bar.
Although authors like Nolthenius(1956) suggest that the quality of the song cycle is far below the level of other of Beethoven compositions and is not very much focused on the voice, there are a lot of qualities in this song cycle. Nolthenius' complaint that sometimes five strophes are on the same melody don't seem to be very relevant; Schubert is doing the same in a lot of famous songs. She also states that the variation in the piano accompaniment has not much to do with the text; I think the analysis above proves the contrary. She also attacks the use of major keys where the text is about "Sehnsucht". In my opinion there is no reason to use minor keys in this context; the choice of keys seems to be very effective in this composition. Finally she attacks Beethoven that the voice is handled like a normal musical instrument. The pizzicato in song 3 and the coda of the last song are used as an illustration for this. Although the difference with composers like Schubert and Schumann is obvious, it doesn't make the song impossible to sing.
Let us finally put the cycle a little bit into context, although doing this well would require much more than is done here.
"An die ferne Geliebte" is the first song cycle using voice and piano and having a coherent structure. Beethoven uses techniques from his instrumental work to create the song cycle. Especially variation of motives and a coherent tonal structure.
If you are comparing this song with for example the Brahms cycle "vier ernste Lieder" the simplicity of this form can be easily seen. Most songs just have variations on one theme, where the voice literally repeats the same theme and the piano makes variations on the same harmonic structure. The harmony is almost always clear and excursions to other harmonies are not extremely far, although fast modulations are sometimes used. These aspects of Beethoven writing were further developed by Brahms, as we have seen in the analysis of the "vier Ernste Gesänge".
Although the text of the Beethoven songs have a loose relationship with the developed musical structure below it, this structure is clearly related with the content of the text. The four motives have an atmosphere that is consistent with the text, and those are developed in the poems that have more or less the same atmosphere. But also specific details of the text are presented in the music: "Seufzer", birds, the lake, the brook, the boat, tears, etc. This relationship with text is developed much further by Schubert, who did related his songs within a cycle more according to atmosphere and perhaps the line of the story than through musical motives. The focus by Schubert is melody in contrast with harmonic structure.
Schumann is much more focused on the in-depth meaning of the poems and the good declamation of the text. The piano is very independent, and mostly tells another story than the voice. Schumann's music is really poetic.
Brahms, finally, is mainly focused on structure, as was Beethoven, but uses much more developed harmonies and rhythmic patterns. Syncope's are very important in Brahms's music.
In summary, Brahms develops structures as used by Beethoven, where a composer like Schubert develops qualities of melody and text interpretation.