Fashion is the engine that drove the industrial revolution.
It is quite simply the fastest changing desire that stretches and pushes the industrial, scientific, and and economic capabilities of a people.
You could get a similar effect by having accouterments likes hammers, staves, houses, etc.. but these change over the course of decades, where as clothes can be more reasonably changed on short time scales. The rich could reasonably do this daily, or every few weeks/months. The poor are generally forced to update every 2 or 3 years. Clothes wear out faster than most things.
Without Fashion your people will either be quite drab, or find alternate outlets such as music, painting, or massive amounts of jewellery to express themselves.
Either way it will likely have a negative impact on your peoples productivity as the tools, and means of production for clothes are similar for many other useful things: bags, sails, tents, and armour. More so with industrialisation like the similarity between the early manual machines for spinning yarn, and potters wheels. Where as painting, music, and jewellery have much fewer such translations.
Humans have moles, scars, freckles, discolourations, rashes, etc... all over their skins. While your elven race seems to have some conscious control over their skins they too will be afflicted by defects. Defects that can cause them ridicule, or worse expose an actual weakness. They will even pay for their own mistakes. What five year old doesn't want a unicorn on their shoulder, that they still want when they are 35?
Simply to avoid embarrassment and/or questions later in life, many elves would wear clothes, even if their skin were flawless.
The society might even evolve to prize flawless skin in a partner. After all, it is a loud declaration of an elf who takes care of themselves. To take care of themselves, clothing to prevent flaws is a no brainer.
A king wears a crown not because they like wearing a metal collar above their ears.
They were it to signal to all around them that they are in charge. Similarly your elves will have need of such symbols.
You could get away with beads, jewels, staves, etc... for some jobs, but most jobs have limitations. A doctor needs both hands for surgery, a cook needs something that won't fall into the food, etc...
The most energy efficient and practical tool for signalling is often a garment of some sort, as it provides a large signal (it covers the whole body) while also not requiring to be held. It provides some modicum of protection from the dangers of the job, while also staying firmly attached to the wearer.