It is simply not true that all living organisms or even most organisms all share some ancestral version of Glycolysis.
Various versions of Glycolysis and Fermentation were later coevolutionary after thoughts which emerged after Respiration; and why? Glucose was not readily available when life first emerged.
As a matter of fact, many Prokaryotes use two far more ancient alternate pathways to break down Glucose: The Pentose Phosphate Pathway or the Enter-Duodoroff Pathway.
Gluconeogenesis, now that’s different. All species can make glucose, and the major part of what many textbooks identify the glycolysis pathway is actually Gluconeogenesis running backwards.
Problem is: the capture of light energy to produce sucrose and other carbohydrates is a highly specialized phenomenon from an evolutionary POV that's not really part of photophosphorylation and photoreduction in Prokaryotes or even Cyanobacteria.
And how about Respiration in Prokaryotes? Most do not rely on reserves of Glucose as a precursor.
What about Eukaryotes? There are many points of entry into aerobic respiration and NOT ONLY Glycolysis.
So why is Glucose given so much emphasis? Glucose is the precursor of Lignin, Cellulose and Chitin. Lignocellulose aka plant dry matter (biomass), is the most abundantly available raw material on Earth for transfer to the second trophic level.