Do Chasidim not wear ties as a rule?
If so, is this by design or an accident of history?
If by design, where can I find said intended reason in print?
Most Chasidim do not wear ties. However there are some that do. Those that do not - do so as "In Der Alte Heim" they did not either. Those that do - do so as "In Der Alte Heim" they wore them.
For example: The Skvere Chasidim wear boots year round. The reason they wore them "In Der Alte Heim" was due to the severe cold weather. However they have continued to do so even in the sweltering hot humid weather in the USA.
It could be based on the prohibition of Chukot HaAku"m, as wearing a tie has no particular inherent practical purpose. See particularly (and ironically) the Beiur HaGr"a YD 178 sk 6.
I have heard from Hasidim that the reason many groups do not wear ties is because the cravat was originally only worn by the priests in those countries they came from. This seems like a very unlikely explanation in light of the fact that it originated as a very trendy fashion statement of first soldiers and then dandies. Most likely, because it was a modern, enlightnement era fashion statement, most of the Hasidim stayed away from wearing it.
The Lubavitcher Rebbe wore ties.
I have read all the above answers, and I think they are all valid, however, if you notice, all the above answers either say: These Hasidim b'Dafka wear ties or these Hasidim b'Dafka don't.
So I think the answer is: it depends on your intention!
Are ties evil? How about a knife or (I dare say)... the internet?
Well, in all the above examples it depends.
None are intrinsically evil, but if used wrongly or with evil intentions then they become evil.
On the other hand, if they are used with good and holy intentions - they become refined and uplifted and have thus fulfilled their purpose in this world.
The life force of all these 'neutral' creations (which can be either refined or become evil) is called Klipat Nogah - Which on one hand is a 'peel' which conceals G-dliness, but on the other has Nogah - light - because G-dliness can still shine within them. (see Tanya Ch 7 for a broader explanation)
So to answer your question:
1) Do Chasidim not wear ties as a rule?
If the Chossid feels that he can't do anything positive with the tie (or if the Rebbe of that Chossid decides this for him?) - then, as a rule - he'd stay away from it. He would argue:
It's only there to serve a fashion purpose! (as @Yahu pointed out)...
It's Chukos Akum! - as @Double AA pointed out)
But if the Chossid feels that he can spread Torah and Mitzvos better with the tie - because it's a kind of a garment which honorable people wear - which would/could mean that people will accept/take more seriously what he has to say - then in this case he would wear one. @Shmuel Brin: This is the reason why Shluchim wear ties (not to be stylish G-d forbid)