Why are exceptionally tall statues of the Buddha and Guanyin built? When I read this article on the tallest statues in the world, I was struct by how many of them were of important Buddhist figures: of the fifteen tallest statues six are of Guanyin (Kannon/Avalokiteśvara), five of the Buddha, and one of Kṣitigarbha, for a total of twelve out of the top fifteen!

Why are such tall statues built? What significance does the height of these statues have in the religious lives of Buddhist adherents?

Or are these statues not built for true religious purposes, but as an unofficial competition between nations, just like they compete over the tallest skyscraper? Nine out of the fifteen were built in the 21th century. Who commissions these statues? Statues of this size would be beyond the budgets of most temples.

See also: this question on why precious metals are used for Buddhist statues.
OP: Why are such tall statues built?

Why do people have statues for the Buddha?
From DN16, the Buddha explained to Ananda, why it is beneficial to have a stupa for a Tathagata (a Buddha):

And why, Ananda, is a Tathagata, an Arahant, a Fully Enlightened One
worthy of a stupa? Because, Ananda, at the thought: 'This is the stupa
of that Blessed One, Arahant, Fully Enlightened One!' the hearts of
many people will be calmed and made happy; and so calmed and with
their minds established in faith therein, at the breaking up of the
body, after death, they will be reborn in a realm of heavenly
happiness. And so also at the thought: 'This is the stupa of that
Paccekabuddha!' or 'This is the stupa of a disciple of that Tathagata,
Arahant, Fully Enlightened One!' or 'This is the stupa of that
righteous monarch who ruled according to Dhamma!' — the hearts of many
people are calmed and made happy; and so calmed and with their minds
established in faith therein, at the breaking up of the body, after
death, they will be reborn in a realm of heavenly happiness. And it is
because of this, Ananda, that these four persons are worthy of a
stupa.

I would therefore extrapolate that the purpose of the statue of the Buddha is similar to the purpose of the stupa of a Buddha, which is, to be an inspiration for peace of mind and happiness.
Today, people in USA remember Martin Luther King, people in India remember Mahatma Gandhi and people in South Africa remember Nelson Mandela. They may have photos or statues of these revered persons put up in public places and treated in a respectable way. The statue of the Buddha is no different. They are there to serve as icons of inspiration.
The Buddha, at least from a Theravada perspective, is no more supernaturally reachable through prayers and rituals, than King, Gandhi or Mandela.

OP: What significance does the height of these statues have in the religious lives of Buddhist adherents?

Now, how was the stupa of a universal monarch or a Buddha built?
From the same sutta:

&quot;But how, venerable Ananda, do they act respecting the body of a
universal monarch?&quot;
&quot;The body of a universal monarch, Vasetthas, is first wrapped round
with new linen, and then with teased cotton wool. And again it is
wrapped round with new linen, and again with teased cotton wool, and
so it is done up to five hundred layers of linen and five
hundred of cotton wool. When that is done, the body of the universal
monarch is placed in an iron oil-vessel, which is enclosed in
another iron vessel and a funeral pyre is built of all kinds of
perfumed woods, and so the body of the universal monarch is burned. And at a crossroads a stupa is raised for the universal
monarch. So it is done, Vasetthas, with the body of a universal
monarch.
&quot;And even, Vasetthas, as with the body of a universal monarch, so
should it be done with the body of the Tathagata; and at a crossroads
also a stupa should be raised for the Tathagata. And whoever shall
bring to that place garlands or incense or sandalwood
paste, or pay reverence, and whose mind becomes calm there — it will
be to his well being and happiness for a long time.&quot;

So, the Buddha stupa was not a simple tomb. Rather, it was a very grand memorial shrine.
Similarly, I extrapolate that the purpose of the great height of the statues of the Buddha is to function as a grand memorial.
It's no different to the giant 38m tall statue of Christ the Redeemer in Rio de Janeiro or the giant statue of Abraham Lincoln at the Lincoln Memorial in Washington D.C.
Doesn't the giant 24m tall statue of the Buddha (the Great Buddha in Bodh Gaya, India) below make you think &quot;this is the statue of that Blessed One, Arahant, Fully Enlightened One!&quot; Doesn't it inspire you and fill you with awe?
Around 2.5km away from this statue, you can visit the Mahabodhi Temple and the Bodhi Tree, the exact location where the Buddha was said to have attained enlightenment. More places of inspiration.
The Great Buddha in meditation pose: