Does it seem strange to anyone else that beyond the extra powers, the main benefit for focusing on a school of magic is that it is easier to copy spells into your spell book when you find spells of that school.  To benefit from that, it discourages you in taking your specialty spells when you level, since, if you take them for free, the benefit comes into play even less.  It seems like specializing in a school should have more incentive to pick spells within your school.  DC Save bonuses, extra spell slots?  These worked well in 2nd ed.

The reason for this may come from the fact that you would know the basic applications of your schools magic already, and don't have to transcribe as much, but you are forgetting that copying spells is entirely contingent on those spells being made available to you by your DM.  If you have a DM with a lenient or generous approach to both downtime and the availability of scrolls/spellbooks for you to copy from, then yes,  it might make more sense for you to focus your level-granted spells on other things.  But not all DMs or campaigns are like that; so in other cases the level-granted spells may be better suited for your school.

Besides, those level-granted spells are a base of the class, not a school specific boon, so you shouldn't expect that to change based on the selection of a school (also, not all wizard subclasses are schools)

This isn't an oversight in the rules;  but it is something to consider as you level, based again on your DM and campaign style.

Actually most of the key abilities from Wizard sub-classes have a strong synergy with spells from the given school, assuming it’s a School of Magic. Just to name a few:

- Sculpt spells from Evocation only works from the aforementioned school. Same thing when you get Potent Cantrip and Overchannel.

- Arcane Ward from Abjuration setup and recharges only if you cast an Abjuration spell.

The downtime learning and cost reduction from your school spells is just a minor benefit.

There certainly is a pretty big difference between the number of spells available at each level for different schools...  there's far far more conjuration and evocation and transmutation spells, than there are any other school, especially divination spells. Different schools have more or fewer options at each level, but if you're not an Evoker or Transmuter or Conjurer, there's a pretty good chance that you'll be faced at some point by there not really being any attractive choices within your school to pay to transcribe. 

It is a minor feature and you play at your own risk by not choosing school spells at level up.

Imagine you are an Evoker and hit 5th level and can’t wait to get your signature spells like Fireball or Lightning Bolt, but you choose two non-Evocation spells at level up, figuring you can copy Fireball or Lightning Bolt spells cheaply. Then your DM doesn’t make a scroll or spell book available with those spells until much later levels. You could end up going through levels 5, 6, and 7 without those signature spells because you chose non-school spells at level up.