If you want people to say thanks, then state that you want people to say thanks. I say thanks pretty much only if no one else has said it yet.
Oh come on, I'm not going to ask people to say thanks! That's just rude and takes away the whole point of a genuine thank you! If you give something to someone, you expect a thanks. But it's completely different if you ask for one.

Mindlessly writing "Thanks" to every giveaway I'd enter is, as the world "mindlessly" might imply, fairly meaningless. At that point, it is arguably less respectful to post "thanks". I've only done a couple of regular giveaways, but I didn't feel bad that most people entering didn't say "thanks".
So you think that saying Thanks is meaningless. I just want to clarify that again: You. Think. That. Saying. Thanks. Is. Meaningless. And now you're actually saying that it's less respectful? Like I've said so many times before, it's better to at least try to show your appreciation rather than do nothing. WHAT HARM DOES IT DO? What percentage of giveaway creators do you think look at their giveaways and say: "Oh no, people are spamming thanks and I don't want their thanks."

I'm even on the fence about saying "thanks" after you win, because my first response on seeing an email from a giftee is to think that there has a problem. I've done more forum key giveaways, where it is nice for the "winner" to say something just so you can mark a key as claimed and people can stop trying.
Wow............I really don't understand you. No seriously, I really don't understand the first half of this paragraph and how it's a valid reason for not saying thanks.

A low "thanks" ratio is also helpful in scanning comments for actual questions or other issues. If you have thousands of "Thanks" comments (due to a mandatory requirement on a long and public or just well distributed giveaway), then it is harder to find legitimate queries and concerns.
If you do want to make posting "Thanks" a requirement, you might want to require "thanks" in particular non-standard forms, so you can filter out the auto-commenters. Those to me are the least respectful.
This is a COMPLETE excuse. I've seen it used time and time again and it has very little weight in this argument. Actual questions or other issues can be addressed in a reply to the first comment or messaged directly to the creator. I mean, I can't believe you actually use this as a reason to be lazy.

Of course most of the above becomes more of a non-issue if you are doing a low entry private giveaway. If you are doing a $100 giveaway to a restricted group that will see a total of 20 entries, well, that is a different world.
Hence the reason I don't make public giveaways. I'm not going to tell people to write a thank you to me. I'm not going to make giveaways for lazy people. I'm not going to make giveaways for ungrateful people. Basically, I'm not going to make giveaways for people who don't deserve them.

I don't post "thanks" in most of the public giveaways I enter but I still think your argument is ridiculous. I am like you in saying thanks if not a lot of people have since in that case it does make a difference to say it but feel that in giveaways where a lot of people have said it already my voice will just be uselessly lost in the crowd.

However, the things you list are just non-sense. Saying thanks is never the less respectful thing to do compared to not saying it. When is a thank you ever taken with dislike?

The "spamming" of thanks doesn't particularly make it that hard to find real issues or inquiries because the message length required to thank someone and to ask a question are different. It's easy to see a longer message in a sea of short ones.

I cannot believe you could be "on the fence" about saying thank you after a win because your personal first response is that there MIGHT be a problem. That's the biggest bullshit ever. I make up for my lack of thanks by making sure that when I win I give a thanks that's more than just a one word message with "thanks". I take the time to let them know how much I am thankful, that I appreciate it, and if it was something I really really wanted then I let them know how much I've been wanting it or how much I've been entering for it. I do all that because there is NO grey area in thanking someone for giving you something for absolutely free.