Well, no, it doesn't. It says that "In infinitesimal small durations there is always one inertial frame, which momentarily has the same velocity as the accelerated body, and in which the Lorentz transformation holds."
Saying that velocity is momentarily the same is not the same thing as saying that the rate of acceleration is momentarily the same. Two cars can both be going 20mph at any given moment when one is accelerating at 10mph and the other at 5mph.
What’s more …an inertial observer always has a proper acceleration of zero. Are you suggesting that there is some infinitesimal small duration of time, in some inertial frame where Earth’s acceleration is zero?
You claim that it is velocity that's decreasing as it approaches c.
You’re right, I should have been more precise and said that its velocity is decreasing relative the rate of acceleration.
It sounds to me like you've made a lot of assumptions about what's being proposed.
I’m just reading the wiki text and the way I read it says that the earth can have a proper acceleration of 1g forever and not reach c because from an inertial frame of reference the proper acceleration will appear to decrease at increasing rates and therefore an inertial observer will never see earth’s velocity reach the speed of light.
Is that a correct interpretation? If it is, that explanation is wrong. The reason an inertial observer never sees earth’s velocity reach the speed of light is because it never reaches the speed of light in the accelerating frame, even though it continues to accelerate at the same rate. How and why that can be true is clearly explained, even simplistically, in the sources I cited. Because the formula for adding velocities must take time dilation into account, an object can accelerate ad infinitum without the total velocity ever exceeding c. IOW, accelerating 100,000 mph will add less than 100,000 mph to the total velocity. Check the formula for yourself and see how it works out if you doubt it.
If that’s the correct interpretation, it also means that even though the proper acceleration will appear to decrease from an initial observer, it doesn’t decrease within the earth’s frame of reference, as measured by an accelerometer, and within its own frame, Earth would reach c.