Are Hand-Based Stat Monsters prone to abuse?
Does anyone have another example or an answer?


I think that yes, they could be abused... but the situation you portray is by itself hard to achieve.

To summon Slifer, the Sky Dragon you must tribute 3 monsters first, something that takes time and surely cards from your hand to achieve.

Next, cards like Pot of Greed that you mention are Forbidden in competitive play (why, check this other post). Unless you want to play Traditional format you can't use cards like that. And even if you did, in Traditional format you would be able to have 1 copy of Pot of Greed, not 3...

Now, regarding Veil of Darkness. Yes, you may draw another card if you draw a Dark monster, but the card also requires you to discard the Dark monster you drew (so no hand number increase). From its text, emphasis mine:


  During your Draw Phase, if you draw a DARK monster(s): You can reveal any number of them; send them to the GY, then you can draw 1 more card.


Finally, there are several other ways to get rid of a monster, regardless if they have 26,000 ATK points:


You can return it to the hand (say, Compulsory Evacuation Device)
You can send it to the GY (say, Dark End Dragon)
You can destroy it (say, Soul Taker)
You can banish it (say, Dark Core)
You can take control of it (say, Creature Swap)


etc... So as you can see, using Slifer and hand-number strategy is not as easy as one may think, as there are several ways to counter those cards, as well as some you thought useful are actually not that useful for this scenario.