Although this has always been assumed to be the case by Einstein and some the earliest adopters of relativity, in practical terms there is rarely the need to consider the propagation of time dilation or gravity.  Since we cannot turn off or otherwise deflect gravitational effect, it is largely treated as static.  As such, there has been a substantial part of the scientific community who have believed gravity to be a static and effectively instantaneous force over distance.

However, the much publicized LIGOS measurements of gravitational waves is the first large scale experiment providing compelling evidence that time dilation cannot move its effect through space any faster than about the speed of light.

Considering that the total universe is estimated to be many times larger than what we can observe, we should expect to continue being slowly "flooded" by additional time dilation as time goes on.

Einstein had theorized the equivalency principle decades before Hubble's theory which states that a change in gravitational potential is observably identical to Doppler effect.  That fact alone brings the presumption that cosmic redshift is primarily due to Doppler effect into question.

However, in the early half of 20th century, the popular belief of astrophysicists (including Einstein) was that the universe had always existed (temporally infinite). There was no substantial evidence at that time to confirm any hypothesis regarding the origin or age of the universe as we do today. It would be a decade after the passing of both Einstein and Hubble before discovery of the Cosmic Microwave Background which would provide the evidence for a finite age of the universe.

Although Einstein showed that there were multiple causes for observable redshift, in a temporally infinite universe there was no reason to consider a cosmic scale change in gravitational potential.  So when Hubble hypothesized that redshift was entirely Doppler driven, Einstein was simply content that the question had an answer.

If those great thinkers knew what we have learned about the CMB and gravity waves over the last 100 years, I am confident they would have come to a different conclusion.

In short, it doesn't.

All hypotheses related to dark energy are attempting to confirm Hubble's assumptions from 100 years ago.  To prove that the universe is metrically expanding has always required a yet unobserved cause. However, there are several fundamental issues with Doppler-centric expansion and dark energy as a whole:

1. Hubble's own theory assumed that there is a curve to the rate of cosmic expansion.  However, all observable evidence points towards a linear redshift trend. Either we are not yet capable of observing the curve, or we coincidentally exist at a period in cosmic history where the curve matches an equivalent linear trend.

2. There is no observable evidence for dark energy, and any study to prove its existence has been inconclusive at best.

3.  It has only been recently that we have observed vast hydrogen clouds around galaxies.  Even in our own back yard, the Kuiper belt serves as an example of only recently observed and measured ordinary matter in our universe.

For certain there is mass in our universe we cannot yet observe, but not because it is of some exotic type.  It will likely all be common particles that are simply not sufficiently illuminated.

1. Dilation flooding should result in a linear redshift value over distance.  This is because as a time dilation field propagates from its source, its influence diminishes over distance per the inverse square law.  However, over time the sources of time dilation influencing any given point in the universe increases with distance per the inverse square law.  Since all observations of redshift strongly correlate with a linear function, observations match the theoretical predictions of dilation flooding.

2. Since dilation flooding is slowly compressing the maximum possible gravitation potential energy, this implies that there should be a history of higher energy events in our cosmic history. Quasars provide such evidence as they demonstrated energy levels beyond what we observe in any more recent cosmic structure.  A wider possible range of Gravitational Potential provides a validation for some of the more improbably extreme behavior observed in many quasars.

3. Dilation flooding is the only redshift theory that does not propose any unknown force or unproven variable.
It requires nothing more than the observable lab proven theory of relativity and a temporally finite universe (e.g. Big Bang theory).  Since relativity has been shown to be undeniably accurate and observational evidence, and deduction strongly points to the universe as we know it being of a limited age, dilation flooding is a logical and uncomplicated conclusion.

In the strictly "metric" sense as hypothesized by Hubble, there is as of yet no evidence to support that as the singular cause of redshift.

However, if one strictly interprets increasing time dilation as a stretching of spacetime, then dilation flooding is resulting in the distance between all points in the universe becoming increasingly distant from each other.

Note that our contributors prefer to model time dilation as a radiated particle field in a fixed metric space.  This allows dilation flooding to be compatible with quantum mechanics as well as field based relativity. That being said, since all current methods for measurement are dependent upon the speed of light, length measurements not adequately adjusted for time dilation or dilation flooding will appear to have changed over time.  This, again, would give the appearance of space expanding over time.