It isn't intended to be fair. The simple fact is that a starting wizard is assumed to have spent time in the college being taught by teachers how to channel, and a few basic spells. They are assumed to have already spent the time and effort, in their backstory.
"During game" a PC that switches will need to buy them because they have to spend the effort and energy. They don't magically "just know" stuff simply because they have switched a career. Of course, as mentioned above, if your story is giving a several-year time-lapse, where the PC gains training in spellcasting, then it would be a reasonable option to give either give them free actions/spell, or give them XP to spend.
Of course, keep in mind that to be fair to other PCs, you should realistically compensate them for their experience during that time frame, if you are giving the new wizard PC free stuff.
I think part of this is to encourage players to start as wizards and stay a wizard, rather than entering or leaving the career willy-nilly. "Realistically", it would be difficult for a PC to switch to a wizard career in the middle of a campaign. Really, a PC who shows magical talent is either whisked away to the colleges, and must spend a few years there training to control their ability, or else they are a "witch".
Without a "time-lapse" to accommodate time in the Colleges of Magic, as a GM I personally wouldn't allow a PC to switch to a wizard career. If they want to be a spellcaster after their first career, they need to go witch.
I suppose, after some thought, for me the only conceivable way a PC might be able to switch to a wizard mid-campaign, is if there was another college wizard present in the party (whether PC or NPC), of a decent rank, to train the PC. Still, the PC would need to learn their skills/actions/spells and wouldn't get them for free.
I'll need to relook at the witch/warlock careers to confirm. I believe that they do get the Petty spells for free, if they start as a Witch. They do NOT start with Channel Power action. All that means is that they must rely on equilibrium to regain Power. They don't have access to Channel Power until they reach Warlock. Of note, Witches can purchase spells from ANY of the Colleges, as well as Dark magic spells (I believe), with their XP.