I very frequently play monocolour; I've
always had a mono-black deck in my arsenal, and there's frequently other mono-colour decks in circulation as well. I currently play
Bruna, the Fading Light on a very regular basis.
Reasons to play monocolour:
1. A general appeals. Usually, it's a unique effect, but not always. Among the ones I have fond memories of,
Selvala, Heart of the Wilds,
Toshiro Umezawa,
Odric, Master Tactician,
Heliod, God of the Sun and most lately,
Bruna, the Fading Light and
Erebos, God of the Dead. I also frequently have a monored deck, though I don't at the moment;
Jaya Ballard, Task Mage and
Neheb, the Eternal were both great. If it doesn't inspire you, that's okay, but it would be ridiculous to claim any particular inspiration is universal. People are different.
2. Though they often pale compared to multicolour considerations, there are some mechanical reasons to play monocolour.
Nykthos, Shrine to Nyx is a big deal.
Gauntlet of Power,
Caged Sun,
Gauntlet of Might (for red),
Crypt Ghast and
Nirkana Revenant (for black) are all very nice and good. For white, I do like to play
Endless Horizons. Some devotion mechanics are also fairly strong (mostly just
Gray Merchant of Asphodel, but
Karametra's Acolyte was no slouch either). Sometimes, there are powerful effects that depend on the number of lands of a particular type you control, as well;
Valakut, the Molten Pinnacle and
Emeria, the Sky Ruin are common enough (and can be leveraged in multicolour even if they are easier/more effective in monocolour), but I would venture that
Scourge of Fleets,
Engulf the Shore and
Flow of Ideas are all very passable.
Reasons to play Monowhite in particular:
1. It's a challenge. The colour lacks draw, and that means squeezing every little bit out of every resource. I think it improves your playskill to try and politic and play with limited resources through a table. It also hones your deckbuilding skills; it gives you some real insight into what kind of metrics you expect out of a card, whether it was pulling its weight, or was overcosted, etc. When you don't get to draw as much, every draw counts.
2. You're seen as the underdog. There is a political aspect to playing a deck that looks and feels overtly weak. For the first dozen or so games with Bruna, people really did leave me alone in favour of greater perceived threats. Somewhat surprisingly, I would end the game with the most lands by a fair margin, and won a disproportionately high number of games with it (somewhere in the order of 75%). Emeria can be backbreaking. So can Avacyn. If you just hit your land drops all game because you have a lot of land search in your deck, you can recast a value general, or a general that admits narrow answers, over and over again.
3. White has some mechanically unique effects, some of which are very powerful. I will freely cede that white is the weakest colour in EDH, ever since red got passable draw. The only thing white has left is the quality of their exile removal, plethora of board wipes, and capacity for life gain (but not really that last one). However, white has stuff no other colour has:
Avacyn, Angel of Hope for blanket and persistent indestructibility, and
Brisela, Voice of Nightmares, who... is a giant mess of things, not duplicated much elsewhere.
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Obviously, the more cutthroat your tables are, the less viable this becomes as players demand hard answers for powerful combos or loops, basically requiring a some majority of the players at the table to play Blue for the flexibility of counterspells. My group can definitely lose under the weight of several recasts of Bruna, but I would not expect other groups to succumb to the same thing.
Sometimes playing Monowhite is all about bringing a knife to a knife fight, you know what I mean?
