Why would this offer of help be attractive?

Question

Spoilers for the The Magician’s Apprentice S09E01 (story 251) below.

Out of all the possible gambits, why did Missy think that this deal would be attractive to the

Daleks?

This is the plea she makes:

Missy: And you know all about those, don't you? This is a TARDIS. With this, you can go anywhere, do anything, kill anyone. With this the Daleks can be more powerful than ever before. You just need one thing...

Clara: No. Missy, no!

Missy: Me! You need me. A Time Lady, to show you how it works. With this and with me, everything can be yours. And you can burn it all, for ever and ever and ever. Or would you rather just kill me?

---

From Utopia S03E11, and later in story 187, we know that Missy can use the TARDIS, so her ability to fly it isn't in doubt. But the benefits a tame Time Lady flying a TARDIS offers a Dalek, they already have:

• The Daleks can Time Travel
The concept of the Time War was that the Daleks could time travel and have since done so numerous times in modern Doctor Who in episodes such as Victory of the Daleks S05E03 (story 205) and Daleks in Manhattan S03E04 (story 182).

• The Daleks can transport troops through Time
Since Resurrection of the Daleks (story 133) have had Time Corridor technology which is shown to be adapt at troop transport across time, and seen as recently as an unfollowable escape route in Victory of the Daleks S05E03 (story 205).

• Dalek Time Travel is at a par with Time Lords'
Previously Dalek time travel was shown to be not as precise as the Time Lords', but Dalek Sec was able to navigate into the Time War as revealed in The Stolen Earth / Journey's End S04E12 / S04E13 (story 198), so around the time of the Time War and after they're technology was comparable to the Time Lords.

• Dalek spaceship design is advanced
As seen in Army of Ghosts / Doomsday S02E12 / S02E13 (story 177), during the Time War the Cult of Skaro was able to create a Void Ship, something the Tenth Doctor declared as impossible:

Doctor: Well, it's impossible for starters. I always thought it was just a theory, but... it's a vessel designed to exist outside time and space. Travelling through the Void.

Answer 1

The TARDIS is more than just a time machine.

• It's a super-duper spaceship that can travel anywhere in time and space.

• Its interior is large enough to transport an army, while its exterior is small enough to be more easily concealable than any Dalek spacecraft.

• Its sentience means that if its loyalty could be won (which would admittedly be hard, for either Missy or Daleks), it could be a valuable ally as well as just a tool, as shown in e.g. Boom Town (series 1).

• It can enable the prevention of time paradoxes, which would give the Daleks more freedom in their time travelling abilities than they've shown so far. Missy knows this, since (s)he demonstrated it in the Sound of Drums arc. _{^{(Credit to @Richard for pointing this out.)}}

With a TARDIS at their disposal, the Daleks would become not just time-travelling Daleks, but beings with the firepower of Daleks and the technology of Time Lords: truly a force to be reckoned with. What surprises me is that they didn't take her up on her offer. But then Daleks aren't always known for their intelligence.

There is a precedent for Daleks making use of Time Lord tech.

In Doomsday (S2E13), the Cult of Skaro has seized a Time Lord prison ship for their own use.

BLACK DALEK: The technology is stolen. The Ark is not of Dalek design.
ROSE: Then who built it?
BLACK DALEK: The Time Lords. This is all that survives of their Home World.
[...]
BLACK DALEK: Time Lord science will restore Dalek supremacy.

Maybe the Cult of Skaro are different, but they at least do not disdain using Time Lord technology. If Daleks have a concept of consistency, they should have jumped at the chance to possess and use a TARDIS, surely much more useful and powerful than the Genesis Ark.

Answer 2

In the The Witch's Familiar S09E02...

Missy tells Clara a story of the Doctor:

Missy: Hush! He's traveling by teleporter. Unfortunately, his teleporter is out of power. Also unfortunate -- he's being stalked by, oh, say about 50 android assassins? I may be rounding up.

[... banter ...]

Missy: The Doctor, then. Surrounded. Outnumbered. Outgunned. And... freeze. Nanoseconds to live. Four, I'd say, being generous. Now, my question is this... How... did he... survive? Oh, come on, Clara! You know him. Consider the Doctor.
Clara: Where did he get that teleport thingy?
Missy: Oh, good, good. He stole one from an android.
Clara: So, I'm guessing he uses the same energy as the android weapons, right?
Missy: Excellent! Not seeing you as sandwiches now.
Clara: OK, then! He uses the energy wave from the android weapons to recharge the teleport bracelet and at the exact moment he's supposed to disintegrate, he actually teleports! Hang on -- that's how you did it.
Missy: No!
Clara: That's how we escaped the Daleks.
Missy: I modified the same principle for our vortex manipulators, yes. Blew them off, I'm afraid. But the Doctor, he improvised it. He must have got through several thousand calculations in the time it takes to fire up a disintegrator. Seriously, what a swot! So the androids think he's dead and the Doctor escapes.

So based on that and the Master's past history on Skaro, e.g. being executed there in the 1996 Movie / Pilot,

having the Daleks accept the offer wasn't the primary goal, so its attractiveness (or lack there of) is somewhat of a moot point. Escape and assisting the Doctor was the primary reason. Missy's plan at the time was to antagonise the Daleks enough into shooting them and facilitating the escape. The exact wording she used was (relatively) unimportant.