/ʝ/ vs. /ɟ/
Phonetically, there is a lot of variability in the realization of the Spanish sound that Wikipedia transcribes as /ʝ/, both between dialects, and in some cases between different utterances made by the same speaker; and there seems to be some unconditioned as well as conditioned allophony (see L2 perception of Spanish palatal variants across different tasks, Allophony of /ʝ/ in Peninsular Spanish, Variation in Palatal Production in Buenos Aires Spanish). So it may not actually be of much pedagogical benefit to use a phonemic transcription that suggests that the realization of /ʝ/ is subject to conditional allophony in exactly the same way as /b/, /d/, and /ɡ/. (Then again, it's also true that /b/, /d/, and /ɡ/ don't have exactly the same patterns of allophony as each other, despite their similar transcriptions; nor is the allophony of these segments 100% conditioned by the phonetic context.)
If we look at things from a phonological or morpho-phonological persepective, there seems to be a relationship between /ʝ/ and /i/ or /j/ in Spanish (probably, there could be arguments about the extent to which this relationship is diachronic vs. synchronic). For example, the word rey /rei/ has the plural form reyes /reʝes/. I would guess that this could be grounds for arguing that a plosive symbol is not the best choice for the underlying representation of this sound, although I have not seen any source that explicitly says this.
In fact, the existence of a phonemic distinction in Spanish between /ʝ/ and /j~i/ seems to be disputed. "The Phonemes of Spanish", by Rebeka Campos-Astorkiza, in The Handbook of Hispanic Linguistics (2012), edited by José Ignacio Hualde, Antxon Olarrea and Erin O'Rourke, says that /ʝ/ may be analyzed as "an allophone of the high vowel /i/" in syllable-initial position (p. 103, 4.2). The contrast between putative minimal or near-minimal pairs like abierto and abyecto can be explained in that case as consequences of different syllabifications. Campos-Astorkiza references work by José Ignacio Hualde that has more discussion of this topic. I also found a bit more information about this in the powerpoint for "The Dialects of Spanish and of Modern Greek – Natural Laboratories for the Generative Phonologist", by Ellen M. Kaisse, which you can download by clicking on this link: Dialects of Spanish and of Modern Greek.
/b/ /g/ /d/ vs. /β/ /ɣ/ /ð/
I don't know what analytical considerations are relevant for /b/ /g/ /d/ vs. /β/ /ɣ/ /ð/; note that the former set of transcriptions is easier to type and uses more familiar symbols (also, symbols that are used in the spelling system of the language), which may give it an advantage just on non-theoretical grounds. Note also that the Wikipedia page you linked to says
Typical phonological analyses of Spanish consider the consonants /b/, /d/, and /ɡ/ the underlying phonemes and their corresponding approximants [β], [ð], and [ɣ] allophonic and derivable by phonological rules. However, approximants may be the more basic form because monolingual Spanish-learning children learn to produce the continuant contrast between [p t k] and [β ð ɣ] before they do the lead voicing contrast between [p t k] and [b d ɡ].
This section references Macken, Marlys A.; Barton, David (1980b), "The Acquisition of the Voicing Contrast in Spanish: A Phonetic and Phonological Study of Word-Initial Stop Consonants", Journal of Child Language, 7 (3): 433–458. If you want to learn more about the relevant issues, perhaps you could read that or find some more recent source that cites it.
Some sources I found in this way that seem relevant: