The Practical Enchanter specifically lists what kinds of bonuses apply to what. The only section listing "Initiative" is the Insight Bonus section. Since Initiative is specifically called out there, separately from "Checks", we know that spells from that book other than Insight Bonus spells do not affect Initiative. Similarly, Saving Throws are specifically called out as being separate from Checks.
The GM may rule otherwise, but that's the way that book is written, so that's how spells from it work.
- Similarly, spells such as
- Benediction specifically calls out Saves, Skill Checks, and Ability checks without mentioning initiative.
- Crushing Despair (like Good Hope) specifies attack rolls, saving throws, ability checks, skill checks, and weapon damage rolls, but does not mention initiative.
- Curse Of Ill Fortune calls out attack rolls, saving throws, ability checks, and skill checks without mentioning initiative.
Nerveskitter specifically calls out that it alters current initiatives. That establishes that spells cast after battle has begun generally do not alter initiatives.
Shock and Awe specifically penalizes initiative, but nothing else.
Cat's Grace adds to Dexterity, and specifically calls out that it affects Initiative and other uses of the Dexterity Modifier.
Initiative checks specifically get their own definition in the rules - "At the start of a battle, each combatant makes an initiative check. An initiative check is a Dexterity check. Each character applies his or her Dexterity modifier to the roll. Characters act in order, counting down from highest result to lowest. In every round that follows, the characters act in the same order (unless a character takes an action that results in his or her initiative changing; see Special Initiative Actions)."
Now, that does classify them in the general category of Dexterity Checks, but then goes on to specify what applies to the roll - the characters dexterity modifier. That's consistent with the various spells. As usual in the System Reference Document, the specific - "Each character applies his or her Dexterity modifier to the roll" - normally overrides the general - "is a Dexterity Check".
And yes, I am well aware of the various arguments that say that check modifiers should apply (and, it appears, in fifth edition they do) - but that really doesn't seem to be the way that 3.5 was written.
On the practical side, given that allowing spells that modify checks will keep changing characters initiatives - thus needlessly complicating an already overly complicated combat system - I think it's a poor idea. It's still ultimately up to the game master though.