This is an interesting question actually.  Depending on the lane surface and the oil being used, it could be possible to cover most of the typical house shots.  This would typically fall into the older houses that still have high friction wood surfaces.  In fact, a local bowling show that is taped near me ended up filming 4 weeks at an older house with a wood surface and most of the bowlers opted for urethane based on the house shot.

So I would look at a stronger urethane ball such as the Pitch Black or the Black Hammer Urethane in the upper end.  Depending on your game, you could throw a stronger layout and/or adjust the surface down to 500 or 1000 and that will give you something very smooth with some backend.

Now alternatives to those balls could be either the Burgundy Hammer or Brunswick Fanatic BTU.  Both of these are slightly stronger than the Pitch Black or Black Hammer Urethane in their covers because they have a tiny bit of resin additive.  But, they would still give you a urethane motion overall with just a bit more in back.  With how the lanes have been where I bowl as of late, I'm actually considering a Fanatic BTU or possibly a Black Hammer Urethane because of how the THS can burn up.

After that, the Purple Hammer Pearl Urethane, Pitch Blue, or Motiv Tank Pearl for when the lanes really become the desert.  This will give you a reaction that gives you more length but still is very controlled in the back.

Just keep in mind that urethane will push oil down the lane instead of absorb.  Therefore, you just have to be careful with how you'd want to play the lanes, especially later on in the league night (usually game 2 and 3).  But it can be done.

I think it would be a mistake.  Having a urethane ball is great when you want to play on the friction, because the response time is much slower than reactive resin. 

However, urethane's strength (slow response) is also it's weakness.  When the lanes open up and you want to create "area" you'll give yourself much more miss room with reactive resin.  If you throw urethane on oil it's likely to go straight. 

I just watched Tommy Jones, who is a very good professional, lose in the tenth frame of the TOC and I felt horrible for him.  He made a tiny move left and his urethane ball went 60 feet...  My heart sunk for him.

One urethane ball can fill in an arsenal, but I cannot see a reason to need more than one.

Thanks everyone. 

I think it would be a mistake.  Having a urethane ball is great when you want to play on the friction, because the response time is much slower than reactive resin. 

However, urethane's strength (slow response) is also it's weakness.  When the lanes open up and you want to create "area" you'll give yourself much more miss room with reactive resin.  If you throw urethane on oil it's likely to go straight. 

I just watched Tommy Jones, who is a very good professional, lose in the tenth frame of the TOC and I felt horrible for him.  He made a tiny move left and his urethane ball went 60 feet...  My heart sunk for him.

One urethane ball can fill in an arsenal, but I cannot see a reason to need more than one.

This is so true.  I currently carry a Brunswick Phantom as my spare ball/special conditions ball.  The ball is fine as a strike ball on our THS, however, once the shot forces me to play away from the pocket, the carry is significantly reduced.  I can play a small swing but as Lane said, you just cannot trust urethane in those instances.

And to be honest, the current urethanes are pretty strong compared to older versions.  I may try out a new Purple Hammer to see how it compares to my Phantom which covers quite a few boards, as much as some of my resins.

As a low rev lefty, I could not go all urethane.  I definitely do not see enough friction for it to happen.

I also agree with what others have said about chasing in and missing out on the carry.  An all urethane arsenal is too limiting.  However, trying it in a non-sanctioned/non-money league would be a fun thing to try.