in 3e and earlier editions cleric was my favourite class and wizard was my second favourite class. Magic was the initial attraction, these classes becoming increasingly powerful each edition was a bonus.
But every new spell increases the potential power of these classes, and the best of the spells tend to be either broken or really really broken.
1st ed level 1 magic users were weak, really weak. They had to hide from everything waiting for the right time to use their single overpowered spell. I will never choose to play a class that weak again.
But the price of playing these spellcasters well in general was ruthlessly rationing spellpower. Hoard spells jealously till they could be cast with maximum effect, and otherwise throwing darts/daggers/ using a crossbow in 3rd ed.
When I saw other players "waste" spells by using them all the time even when not needed, using multi target spells on single creatures, Fort spells on creatures who obviously had good Fort saves and generally being flashy and ieffectual, it was hard not to react loudly in protest.
The most fun part of playing a wizard in 4e was having unlimited cantrips and at-will attacks. It felt far more magical to me than desparately hoarding spells until their use could be justified.
I would gladly accept weaker spells as in 4e if every full caster class gets unlimited use of appropriate cantrip magic and some sort of at-will attack.
In previous editions of D&D I hated lack of balance, the alternatives of not playing at full power or of completely dominating play and making the non-casters irrelevant. And sometimes I like to play fighters and want continue to be effective with rising level.
I don't see secrecy as a way of providing magical magic. It never lasts.
What feels magical to each player is intensely personal, the only way I can see is for referees to find out what each player of a spellcaster feel is magica in terms of the feel and appearance of magic and try to provide that sort of presentation in the game. Thematic description of magic, allowing casters to have their own style of magic in terms of how it looks, sounds, smells, these are the most balance way of providing personalised magic to players without affecting the power of the magic itself.I have increasingly done this since 2e - some players love it, others aren't too bothered.
But NPC casters have their own flavours of magic as well, and the PCs learn to recognise some of them over time, and react accordingly.