Ultimately a DM decision, but it's more than reasonable for it to provide some illimunation
The case for light: Fire provides light.
This one is pretty simple. It's a bonfire. Fire has light. Pretty simple.
Bright light lets most creatures see normally. Even gloomy days provide bright light, as do torches, lanterns, fires, and other sources of illumination within a specific radius. (Basic Rules, p. 68)
The problem arises in how much light ("specific radius") it gives, and that's entirely up to the DM to determine. It can be as much as or as little as they'd like and it can be narrated in either direction. (For reference, a torch's specific radius is 20' bright light, and 20' more dim light beyond that).
It's frustrating that the spell (and other adventure modules) references "bonfires", but there are no specific mechanics around them. There are also references to campfires which have the same problem. It's fine that it's up to the DM, but it makes things squirrely when there appears to be a mechanic (bonfire/campfire), but no specific rules for their radius.
The lack of clear illumination radii can make it possible for another reading of the spell that is significantly stricter.
The case for no light. A very strict reading that requires that the mechanics for a given spell/effect/item are completely provided.
But is it? It's magical fire and may have different properties. In fact, there are items like the flame tongue (DMG< 170) and the spell flame blade (PHB, 242) that specifically say how much light the magical fire provides. This suggests that in order for magical fire to shed light, it must be included in the description.
At a top level magical fire is distinct and the properties it has are determined by the text of the spell. Some magical fire provides light because it says so. Other spells don't state that there is light, but there is still fire.
Because of the fact that there are specific examples of fire spells that provide light, the implication is that fire spells that don't state they provide light don't provide light. Otherwise, why have the specific light mechanics for those that do?
Create Bonfire doesn't say that there is light. Just that it is magical.
Spells do what they say, and no more. Create Bonfire (Elemental Evil, 152) states:
the magic bonfire fills a 5-foot cube
This is a magic fire, and not a real fire. This magic fire may simply not shed any light, or not enough to be of any mechanical consequence. There are spells that utilize fire AND provide light, but they are a small subset of the fire damage spells and Create Bonfire is not included in them if looking at RAW this strictly.
If magical fire always provided light, then it wouldn't have been necessary to include it in the spells that have it. You either got it or you don't. And this don't.
Comparing against similar spells
Mechanical Consequences may be the guide here. There spells that deal fire damage that do not also have a light aspect to them. Some do have light, like Fire Shield and Produce Flame.
In areas where there is darkness, this is going to make a difference as an extra bonus to the spell that isn't actually there.
If you look at Fire Shield (a 4th level spell), you get both Light and damage.
Produce Flame (a cantrip), gives you Light and 1d8 damage (increasing with levels). Once the spell is used for damage, it ends.
Create Bonfire (a cantrip), gives you the same damage structure of Produce Flame at the same cost, but the trade-off is that Create Bonfire remains after dealing damage. Adding Light increases the value of Create Bonfire because now you've got the damage of Produce Flame, but you can keep it going for the duration.
Why not allow it to shed light?
At face value, it probably wouldn't do much harm to allow some light since it creates a fire, but there may be an increase in the spell's value if you include illumination with it.
Choosing Cantrips is a cost in itself. You are often limited by the choices you've made and can't swap them out when leveling. If you can get a single cantrip that sheds light and can deliver damage over the duration of the spell,then this increases the value of Create Bonfire.
Ultimately, it's very reasonable and makes in-game and mechanical sense for it to provide light. But it's also reasonable to read this very strictly and only provide mechanics for what's described specifically in the spell's text.