A reusable bottle is among the most recommended items for a traveller. Whether it removes any plastic from the system depends on conditions at the destination rather than on the bottle.
The bottle solves the container, not the water
A refillable bottle replaces disposable containers only if there is something safe to put in it, and in many destinations tap water is not reliably potable for a visitor.
Travellers without an alternative buy bottled water, and the bottle in the bag becomes additional weight rather than a substitute.
This is why refill advice succeeds in some regions and quietly fails in others, with no difference in the traveller's intention.
Treatment shifts the constraint but does not remove it
Portable filters remove bacteria and protozoa, and ultraviolet devices or chemical treatment address viruses that filters may pass.
Neither addresses dissolved chemical contamination, which is a real concern where water passes through industrial or intensively farmed areas.
Treatment also requires a source. In a city that means access to a tap, which is straightforward in accommodation and much harder during a day out.
Refill points depend on someone paying for them
Public fountains, station taps and café refill schemes exist where a municipality or a business network has funded and maintained them.
Maintenance is the harder half, since a fountain that is broken or of uncertain quality is worse than none because travellers stop trusting the network.
Where such infrastructure is absent, individual behaviour cannot substitute for it, which is why refill culture is uneven between neighbouring countries.
Some destinations have solved the supply side
Island and remote destinations that import bottled water at high cost frequently install their own treatment and bottling, supplying guests in reusable glass.
The economics favour it strongly, since shipping water is expensive and the empty containers must be shipped back out again.
Where this exists, the traveller's bottle works exactly as intended, which is a function of the destination's investment rather than the traveller's diligence.
What travels well regardless
A bottle remains useful even in difficult conditions, because it can be filled from a large container at accommodation, which is cheaper and produces far less waste than individual bottles.
Buying the largest available container and decanting is the practical compromise where treatment is not feasible.
The broader point is that most travel waste is determined by the systems at the destination, and individual equipment helps only where those systems already allow it.