AoE spells originating from self
You would need to consider how something like Thunderwave or Word of Radiance worked, because having them affect everything in line of sight is a pretty huge buff, and having them touch only is a pretty huge nerf.
Range self buff spells balanced for caster class
A spell like Mirror Image is balanced to protect a caster who is otherwise weak when attacked. There may be exploits around casting self-buffing spells on other classes where they could synergise very well with higher armour class, extra attack or other features. This synergy will happen at lower levels than equivalent multi-classing, so will be more impactful.
Range self spells with concentration
Some powerful effects are balanced by requiring concentration. When the spell has range of self and is useful in combat, the caster will now have the option of casting it on someone else and reduce or avoid the risk of losing the effect by taking cover. A good example of this kind of spell might be Vampiric Touch or Hex.
Longer distance spells
I would assume Teleport for example would keep the range?
Spells of similar natures and different levels
How would you separate Misty Step and Dimension Door if that both have the same range?
Divination spells
How would divination spells like Augury work that just give you answers? There is nothing to touch or see as a target. Or spells like scrying, arcane eye, and clairvoyance, whose purpose is to provide information beyond line-of-sight?
High Ground
A high vantage point provides significant advantages. I picture a wizard in a plane, with a good pair of binoculars, sniping the king from tens of miles away. ... or possibly blowing up the enemy's satellites from the back of a pickup truck.
What even is line-of-sight?
"Line of sight" may open a Pandora's Box of ad-hoc adjudication that the medieval/renaissance-flavored standard D&D settings avoid by their normal tropes.
Does line-of-sight extend around corners if there's a mirror? Does it pass across a live video feed? Does it cross windows? Does it cross one-way mirrors (if so, does it cross in both directions)? Does it penetrate illusions or holograms?
... though, see this answer for a counter-argument to (some of?) this section.
Who is "you" for secondary effects of self spells?
Spells with range self use "you" to describe effects that impact the caster, and this will need adjudication. For example the spell Scrying has these modifiers:
Knowledge Save Modifier:
Secondhand (you have heard of the target) +5
Firsthand (you have met the target) +0
Familiar (you know the target well) −5
Seems like those "you" would refer to the touched creature, since it is directing the use of the spell?
However:
On a successful save, the target isn’t affected, and you can’t use this spell against it again for 24 hours.
Seems like this "you" should be the caster? Otherwise the group could try multiple times to target the same individual, working around the limitation.