What reasons does Hortensio give for wanting to marry the widow in Shakespeare's The Taming of the Shrew?

As Hortensio watches Lucentio woo Bianca (with some biased
reinforcement from Tranio)—in Act Four, scene two, of Shakespeare's The Taming
of the Shrew—the man pretending to be a music teacher to gain Bianca's love
finally swears that he has had enough.

First, Hortensio
admits that he is not the music teacher that he pretends to be.
Hortensio agrees with Tranio that Bianca lacks loyalty. It bothers him that Bianca would
prefer a man of lower social standing (Cambio, who is really Lucentio) over him. When
Tranio (pretending to be Lucentio, another suitor—in support of
Lucentio's pursuit of Bianca) swears he will
no longer pursue Bianca if Hortensio will do the same, Hortensio joins him, swearing the
he will stop his attempts to woo Bianca, finding her not the woman
he believed her to be.

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TRA:

Signior
Hortensio, I have often heard

Of your entire affection to
Bianca;

And since mine eyes are witness of her
lightness,

I will with you, if you be so contented,
(25)

Forswear Bianca and her love for
ever.

HOR:

See,
how they kiss and court! Signior Lucentio,

Here is my hand,
and here I firmly vow

Never to woo her no more, but do
forswear her,

As one unworthy all the former favours
(30)

That I have fondly flatter'd her
withal.

Once so sworn,
Hortensio announces that he will marry a wealthy widow whom he has only known a short
time, who has loved him as much as he has loved Bianca. He promises that from now on,
when searching for love, he will look for kindness in women, rather than their beauty.
I.e., he will look for the beauty within, rather than outward
beauty.

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HOR:

For
me, that I may surely keep mine oath,

I will be married to
a wealthy widow,

Ere three days pass, which hath as long
loved me

As I have loved this proud disdainful
haggard.

And so farewell, Signior Lucentio.
(40)

Kindness in women, not their beauteous
looks,

Shall win my love: and so I take my
leave,

In resolution as I swore
before.

It would seem with
Hortensio's departure that the competition Lucentio has faced has been reduced to make
his pursuit of the lovely Bianca that much easier.