Healing surges were a purely mechanical invention serving a gamist purpose: being at full health at the start of any given encounter.
This is neither the function not the purpose of healing surges.
This is the function and purpose of the short rest mechanic. Short rests allow characters to restore their own HP and encounter-based abilities without expending powers or non-renewable resources (potions, etc.). By actually being short, they are indeed capable of being taken (and intended to be taken) after every encounter (whether that is a combat encounter or not) which expends the sorts of resources which you can use it to recover.
The short rest mechanic is not contingent on the existence of healing surges, nor are healing surges contingent on the existence of short rests.
Each of the facets of the 4E system of healing could (and in some cases, in other systems does) exist independent of the others. Conflating the various aspects does not aid fruitful discussion.
The primary function of the healing surge mechanic is to place a cap on the amount of HP a given character can recover in between extended rests. This prevents parties from stocking up on cheap healing resources (potions, the previously ubiquitous Wands of Cure Light Wounds) and extending the adventuring day indefinitely, as well as introducing a resource management aspect to all classes.
There are ways within the system to augment (Healing Word and its ilk, feats, items, racial bonuses) the amount gained when using the surges, for those who seek to be more efficient in managing those resources.
There are also ways to bypass the limit, ways that tend to be subject to strict limits themselves (certain Cleric daily attack and daily utility spells), with most exceptions that slipped through having been erased in errata and updates.
The secondary (and largely incidental and unnecessary) function of healing surges is to be a convenient shorthand for a chunk of hitpoints. Without the goal of the daily limit/resource management aspect, there'd be no real need for this aside from the space saved by making '25% of maximum hit points, plus appropriate modifiers' into a less wordy term of art.
Proportional healing doesn't require the existence of healing surges, nor did healing surges necessarily need to be proportional. They could just as easily have been Next's class-based hit dice, or a standard hit die for all characters, or a universal constant (10 HP, for instance).