Sure! ... but why?
But what even is a good size for a familiar?
Smaller ones can be carried easier both physically and by magic, which includes teleporting with them. Generally they are inconspicuous. They are also generally better at reconnaissance, getting into places and being much less likely to draw attention. Some of them are also surprisingly effective ambush/assassination capable. Generally this would be venomous ones, though most can be build to do this. A cat with PUaH and Razor Claws can do a lot of damage from ambush.
Larger ones are more combat capable and might be able to serve as a mount. Kind of at a loss for other advantages of larger ones.
A higher Might is something with mainly advantages, unlike a higher Size. Higher MR. More powers and larger might pool. Their drawbacks are all related to the process of bonding. Harder to do it. Harder to find and befriend. Those drawbacks give the lower Might familiar its only advantage, as pointed out by Itzhak above.
Honestly though I find going for the familiar with maximum power (whether that is maximum combat capability or Might) feels gamery to me. A good familiar should tell you something about the Magus, expand stories, and provide a good role playing subject. They are supposed to be a Magi most trusted friend.
If a player wants one with a lot of "Powwa" (high Might, larger, lots of useful powers) then they had better spend several sessions worth of effort and seasons in game working on getting one. Compare that to getting a common one such as a Hermetic Cat, in which if your Covenant does not have any then you just have to visit a Covenant that does or go to a Hermetic fair.
Lots of Covenants have small populations of some animal with Might. Cats and ravens are the most common. These are all generally of the "Might = 10 - Size" type and what someone should get without devoting lots of game time to the hunt/befriending process.
EDIT: I am also a big fan of having another player build and play the familiar for a Magus. Our table uses the suggestion from RoP:M (p.34) that a familiar build/played by the player of the Magus is Grog-level and one build/played by a different player is Companion-level. You can bump things up one level by playing several sessions. For an average power game, the Mights are 3/10/20 for the three levels.
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A higher size comes with some flaws like you say - hardly subtle, for one. On the other hand, higher size means it survives in battle. This is not something you want on most magi, but a professional demon hunter or hoplite-type character might want a familiar that can come in battle. Additionally, some animals just are large by nature. A horse/unicorn/pegasi or a lion could be fun on some characters.
Beyond what I just said and what Troy said... sometimes a magical animal is introduced in a story and you just go Wow! I want it!
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this is true. Argument valid.
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That is very true.
My idea, and several replies have already been going in that direction already, is that very large and/or powerful familiars are not the norm.
Familiars are useful not only because of thoose factors, but rather:
- The Cords you forge - which can be enhanced over time, to take advantage of
*The natural abilities, virtues, and qualities of the animal - which can be found in small/weak ones as well
*The enchantments you put in - again, over time you can make more and better ones
That being said, you don't have to wait until you are very powerful to do it. As soon as you can find and bind one, you'll reap the benefits.
And if you during a story find a large and powerful beast - go for it, at become famous for it.
In the ideal world, the troupe has thought about and discussed long term goals and wishes:
Troupe member 1: "Imma gettin' a cat!"
Troupe member 2: "Nah, I want something cool and big for Bigshottius of Flambeau"
Troupe member 3: "Do you want me to run a plotline about this?"
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Quite. In particular it allows a magus to use the familiar's MR instead of their Parma.
For younger magi with little Parma this might be a decisive boost all day long, and even for elder magi with strong Parma and knowledgeable enemies it is a welcome protection when their Parma just expired or got dispelled.
Has anyone played a Merinita who is bonding faeries as familiars?
If you have or if you have thought about it, what considerations are you taking into account?
How have you decided on which faeries to bond?
Asking for a friend. 
Actually, I'm currently playing a fairly early career Merinita in 1013 who is thinking along these lines.
Not in my personal games, I have not seen it. My November Maga had a faerie familiar. Biggest advantage I could think of is with faeries you're not bound into animal forms. Josie had a shapeshifting ragdoll as her familiar.
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We balance it in game. The mightier the creature, the more they pull their weight.
They want to consume more vis and want you to invest specific effects that benefit them. They ask for more of your time and if not given, they stirr trouble to grab your attention
At some point, Dragon & the like, the Magi might end up being the Familiar of the Creature...
W
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I am playing a merinita, and she has z faerie dog that she plans to bind, but hasn't done it yet
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I recall finding it fascinating the times i read it, but I've never used it myself, nor seen anybody do it in a saga.