There are several reasons The Doctor would decide against building a Paradox Machine:
He doesn't know how
The original Paradox Machine was created by The Master. There's no reason to suspect The Doctor has the knowledge required to build a Paradox Machine at all.
In "The Girl Who Waited" (S6, E10), The Doctor says he can use the TARDIS to sustain a Paradox allowing two Amy Ponds from different time streams to exist simultaneously, but later reveals this to be a lie. This could mean that the TARDIS by itself isn't capable of sustaining the paradox, or that it could, but The Doctor doesn't know how to make it.
He'd have to effectively destroy his TARDIS
In order to construct the Paradox Machine, The Master had to cannibalise the TARDIS, taking different parts and reconstructing them to allow the paradox to occur. So to do the same, The Doctor would have to also modify his TARDIS to the point where it no longer operates as a TARDIS. I don't believe he would ever consider doing that to ol' "Sexy".
It's not a permanent solution
Anything that anyone does while under the influence of a Paradox Machine is reversed the moment the Paradox Machine stops working. In the case of The Master, an entire Earth Year was undone after Jack shot it, and all the Toclafane were sent back to the end of the universe.
So if the Paradox Machine The Doctor builds stops working for whatever reason, be it damage, or a simple malfunction, or even just a companion talking sense into him, anything he does would get undone. He could save every living thing in the universe a million times over and it would get reversed like it never happened, though being at the centre of it he'd still remember everything.
It's too much power
The Doctor has been tempted this kind of power many times before. For example, just in the modern series, he was offered The Skasis Paradigm by Lassar
DOCTOR: I could save everyone.
DOCTOR: I could stop the war.
"School Reunion" (S2, E3)
He briefly gave in and decided to become The Time Lord, great decider of who lives and who dies, before being slapped round the face with a lesson in morality
DOCTOR: We're not just fighting the Flood, we're fighting time itself. And I'm gonna win!
DOCTOR: For a long time now, I thought I was just a survivor, but I'm not. I'm the winner. That's who I am. The Time Lord Victorious.
DOCTOR: I've gone too far. Is this it? My death? Is it time?
"The Waters of Mars" (2008-2010 Specials, E3)
And the most recent example, he was given an army of Cyberman by Missy for his birthday
MISSY: An indestructible army to rage across the universe. The more they kill, the more they recruit. Happy birthday. Oh! You didn't know, did you? It's lucky one of us remembers these things.
DOCTOR: All of this. All of it, just to give me an army?
MISSY: Well, I don't need one, do I? Armies are for people who think they're right. And nobody thinks they're righter than you. Give a good man firepower, and he'll never run out of people to kill.
DOCTOR: I don't want an army!
MISSY: Well, that's the trouble! Yes, you do! You've always wanted one! All those people suffering in the Dalek camps? Now you can save them. All those bad guys winning all the wars? Go and get the good guys back.
DOCTOR: Nobody can have that power.
"Death in Heaven" (S8, E12)
Ultimately, he always ends up refusing the power, because he realises it's just too much for a single person to have.
In the grand scheme of things, it's kinda rubbish
Of all the various ways The Doctor could become an omnipotent deity ruling over the cosmos, a Paradox Machine is really one of the worst ways he could go about it, even if he wanted to.
I'm sure there are other reasons, but I think it's safe to stop at five.