Amulet of teleportation allows you to move around faster on bigger maps and generals can use cloak of night to catch escaping demigods or flee.

Anklet/Blood are both solid choices, but there are several other worthy favor items.

That's okay.  I don't mind if you run away from me every fight.

If I buy BotF and you buy Anklet, I'm going to have about 50% more HP than you at level 1. Fifty. Percent.

For melee DGs than need to get their hands dirty, you really have to go with BotF otherwise you'll just get bullied around in every fight you have with people that do have BotF, especially early game. Losing early games have a habit of turning into losing end games, if you hadn't noticed.

However, Anklet is good for harassing DGs like Reg or TB, as it allows them to stay out of melee range. 

I love putting speed items on erebus and regulus. I was messing around with playing an erebus that used boots of speed, swift anklet, wand of speed, and journeyman treads and did nothing but run around the map spamming bite, mass charm, and having bishops (Those things waddle fast!). I think teams benifit from having one guy with a speedy build, the mobility helps for the non-lane flags and ganking.

Keep in mind, you can't run either without some significant beatdown.

   I constantly get stuck in this never ending love hate for anklet.  Buy anklet and get beaten heads up 1 on 1 vs blood user.  Don't buy anklet and constantly get run away from by anklet users in a winning fight.  It always feels like a grass is greener situation to me.  Plus anklet is seductive for flag capping, shopping, harassing.  It's so hard to resist it hehe.

It's useful but nowhere near the best favor item.

The huge problem with amulet of teleportation is that it shares a cooldown with teleport scrolls, making it fairly useless overall. It just becomes a replacement for scrolls and allows you to save money (even then I prefer scrolls because their cooldown is shorter).

Cloak of night is nice, and I've played against one Erebus who used it in combination with bat swarm to cover large distances quickly, but besides that, the small distance you teleport with cloak of night is often times not enough to compensate for being a lot slower.

On the contrary, I would argue that the most important ability of melee characters is their ability to run away quickly due to the fact that being in melee makes it harder to open up the distance between you and the enemy should the need arise. This is why I find it extremely easy to ambush melee characters without Swift Anklet for instance - if they don't see me coming from a distance, then it is too late for them. Their 800hp does not save them, whereas extra speed almost certainly would.

Also having 50% more hp at level 1 is mostly meaningless. In my experience that difference closes down really quickly as other people catch up with regular items.

Think about it this way: it costs me only 1750 gold to get the +600hp +10hp/sec armor. Whereas it costs you 6750 gold to get Journeyman Treads. Considering this, why would you settle for BoTF? The advantage it offers will be gone very very soon.

Flip side of the coin: swift anklet allows you to take risks you otherwise would not take (and get more kills), and get out of ambushes that you would otherwise have died in. It is not really a beginner vs. pro thing. It's just that +15% speed makes a huge difference and offers plenty of advantage throughout the entire game, whereas a gap of 800hp is pretty easy to close with cheap items.

My movement speed has never been more then 6.0 in any game I've played.

Health is very important for (obviously) staying alive during large engagements where you have to stand and fight either because there is a vital objective to seize or defend or because you are stunlocked or snared and don't have a choice in the matter. 800 health is a colossal amount of health and will always help you win battles or at least get out alive. As an added bonus, it adds to your overall health regeneration (priests heal a %). 

Having 50% more health at level 1 is most definitely NOT meaningless. It guarentees me that all else being equal, I will *always* win any engagement against an identical build sans Anklet. The Anklet user will be able to run, but the BotF user will not care, and will happily control the lane and farm the creeps while the Anklet user pouts in his tower.

Eventually you are correct that 800 HP becomes less impactful as people add Nimoth, Unbreakable, etc to their arsenals. You are even right that once you have enough money you can form vastly superior combinations through Anklet + Narmoths which comes out way ahead of BotF + Boots. However, you neglect the utterly gimped nature of the Anklet early on. Anklet's superior chasing power will never matter during that time because there is no way to force the BotF to run because you will lose every fight. By the time you have Anklet + Narmoths, you'll be so far behind that it wont matter.

All of this is assuming competent players btw. No one cares if you can force a noob BotF user to run, despite your Anklet.   

For generals, Cloak of Night is infinitely better for escaping ganks or finishing for a kill

One very feasible alternative to consider is the Wand of Speed trinket. The cooldown's not too bad, and always seems to be available when it's really needed. It's +25% movement rate, and even with Rook I can usually run down fleeing enemies. Of course, this has to be bought with precious gold in-game but adds other possibilities to consider for a favor item.

I use it on Queen and kite all the time.  I am able to deal with early game melee'rs quite effectively, and I much prefer to fight a melee'r that has blood than swift.  If they have swift my margin for error decreases dramatically.

I don't think swift is the best favor item, but i think it's one of the best for the ranged characters.  (All 3!!)