Well, for starters, theophoric elements like -el or -yahu appear mainly on verbal and adjectival hosts, also commonly on nominal ones, and it is quite rare when two DNs occur in a possessive relation. But you just don't get three DNs concatenated together without any possessive or other semantic relation. What is "Israel" supposed to mean, after all? "El is Re is Isis"? Or "Isis' Re's El"? It is nonsensical. Look at all the PNs in the OT and throughout ANE literature. Some examples with theophoric elements:
Marduk-epiri "Marduk fosters me," Dio-trephes "Nurtured by Zeus", Aper-el "Fostered by El," Apra-baal "Fostered by Baal," Hayab-ilu "Where is Father El?", Sakar-il "El has Favored," Ummi-balat "Balat is Mother", Ummi-Ishtar "Ishtar is Mother", Aduna-Addu "Adad is Lord", Rim-Addu "Wild-bull of Adad", Anat-umma "Anat is Mother", Shapshi-abi "Shapsh is Father", Bali-erah "Yerih is Lord", Ya-'qub-el "El protects", Ya-'qub-har "Horus (?) protects", Shaddai-'or "Shaddai Shines", Apollo-genes "Beget by Apollo," Dio-dorus "Gift of Zeus," El-natan "Gift of El," Yeho-natan "Gift of Yahweh," Jerubbaal "Established by Baal," Jeru-salem "Established by Shalem", Eli-sama "El Hears," Eli-melek "El is King", Yeho-el "Yahweh is El", Eli-ezer "El helps", Ishma-el "El Hears," Yer-baal "Baal Contends," Peni-el "Face of El," Qaws-natan "Gift of Qaws", Qaws-gabri "Qaws is Mighty", Neri-yahu "Yahweh is my Lamp," Berek-yahu "Yahweh has Blessed", Yerahme-el "May El be Merciful", Hanan-yahu "Yahweh is Gracious", Baal-hanan "Baal is Gracious", Azar-yahu "Yahweh Helps", Gedel-yahu "Yahweh is Great", Zehar-yahu "Yahweh Remembers", Pela-yahu "Yahweh is Wondrous", Mattit-yahu "Gift of Yahweh", Milkom-or "Milkom Shines", El-yasha "El has Saved", Baal-yasha "Baal has Saved", Yahzi-baal "May Baal See", Abd-Ilib "Servant of Ibid", Zidqi-yahu "Yahweh Vindicates", Sin-uballit "Sin Gives Life", Nabu-naid "Nabu is Exalted", Nabu-apla-usur "May Nabu Help the Son", Weser-Anat "Anat is Powerful", Sebek-emsaf "Sobek is Protection", Sekhem-re "Re is Powerful", Seqenen-re "Strikes Like Re", Amen-hotep "Amun is Satisfied", Thut-mose "Born of Thoth", Nebmaat-re "Re Loves Truth", Akhen-aten "Servant of Aten", Tutankh-amun "Living Image of Amun", Hor-emheb "Horus is Jubilant", Ra-messes "Born of Re", Menmaat-re "Eternal Justice of Re", Meri-amun "Beloved of Amun", etc.
In Isis-Re-El, there is no predicate and neither is there a possessive relation. And I have yet to see an instance of three DNs in a single PN or GN (geographical name). I think what you have in mind is a basic conjunction of the three names concatenated together. But there is indeed special syntax for linking DNs together without a predicative relation: the conjunction w- "and" is used. Thus we see examples in the Ugaritic and Eblaite literature such as Athtar-wa-Athtapir, Kothar-wa-Hasis, Yamm-wa-Nahar, Nidakul-wa-Besal, Resheph-wa-Adama, and Agu-wa-Guladu. On this basis we might expect Is-wa-re-wa-el, except I have never seen an instance of three names conjoined together, and neither do such conjoined DNs ever occur as toponyms or ethnonyms. The conjunction of two Egyptian DNs with a Semitic DN is also unusual.
So without even looking at the evidence showing that Israel is a well-formed Semitic theophoric name from a normal verbal root, we can see how implausible the suggested meaning is. And I have looked at many reference works on the subject by well-esteemed philologists (cf. Skinner, Driver, etc.), and no one I know has suggested such a strange and unusual etymology of the name.