It's not a question of bkb or linkins. You can make both, they stack fine, there is no redundancy.
I simply believe that linkin's is a generally strong good item, which is apparently a minority view. Anyway, here is my whole thought process, probably TL;DR for many but I am bored at work so I am going to write it out anyway. I'm not trying to rekindle the argument, I know the majority view and I'm not going to try to change it, I just feel like putting my thoughts into text.
Maybe my medium games aren't up to the measure of a high or very high game, but this is typically how they play out.
Game start, I buy some initial items, which normally need to include regen/sustain items. Obviously this depends on hero, lane, and role.
Anyway, it's fairly often some combination of circlet, gauntlets of strength (if I am planning on making an urn or drums later), slippers of agi, ring of protection, ring of regeneration, a basic courier, tango, salve, clarity potion, and/or stout shield.
However, in an all random game or a game in which I choose to random, I'll also consider a Ring of Health is a viable start. Since I prefer to play all random, this occurs a lot more often than not. Now maybe this right here is where I'll get called a noob, maybe RoH first item is considered bad and terrible, but it works for me. Against a balanced lane, it gives me a huge edge because I can harrass and trade blows but I will regenerate through the damage much faster than my lane enemy, and eventually I can push them out or kill them. In an inbalanced lane in my favor, it just solidifies the domination. And in an inbalanced lane against my favor, it lets me hang out and at least get a few last hits and some xp instead of being completely dominated and forced back and denied all game. In my general experience, RoH as a first item with random gold is perfectly viable and even a good choice in many games.
So, I start with a RoH. If things are really rough and it's not enough to cover my needs I'll buy a tango or two and have the courier send it down while laning, but that isn't usually necessary. The game goes on, and I farm gold as well as I can. Start RoH, base boots are usually my next purchase, and then upgraded boots. I often go tranquility boots (which are eventually disasembled to upgrade into treads or travel) when I do not start RoH, but with RoH I can go straight to powertreads. This saves a little bit of gold because I don't lose gold on reselling the tranquility boots parts.
From here, my next purchase depends on the game. If I am not being pressured at all, but I could use more mana regen, as is the case with most heroes, I will buy a voidstone to finish perseverance. 875 gold for 10 damage isn't a great value, but given the mana regen as well and saving a valuable item slot, I like to get it when I can. The doubled mana regen can make a huge difference for some heroes, allowing farm or harass via spells twice as often.
Other possibility, if the lane is kinda tough, and if the enemy team has a lot of busty damage, I will often go for a cheap item first. Bracer into drums, or gauntlets into an urn, or wraith band into ring of aquila, or start building oblivion staves if i am playing an int carry or semi-carry or a clinkz.
In any case, I will almost always eventually upgrade the roh into a perseverance, unless the game dictates that mana is unimportant (kotl on my team, I happen to be playing a hero with no real mana issues).
Most games, at this point, are turning into constant ganks and as towers start to fall sitting in lane becomes nonviable. Because of this, I don't usually go for a damage item right away. On the other hand, farming up 2100 gold for an ultimate orb, without dying, can be tough. If there is a viable strong item for my hero that is made up of cheaper parts, I'll probably build it next. If not, or if I have a great farming game and can farm up 2100 gold fast without playing too risk, I'll go ahead and buy the ultimate orb right off.
At this point, it's basically a no-brainer. If an ultimate orb is worth 2100 gold, then the upgrade to linkin's sphere is a god damn bargain at only 1350gold, considering it gives you a full half the stats of the ultimate orb, and gives you a minor 1 hp regen and 25% mana regen, and gives you spellblock every 17 seconds. And, crucially, it does this all in one slot. The stats alone are nearly worth the price, when you do the math you can see the spellblock ability is basically being handed to you for free.
To me, it's a great next item after getting the basics, because it's giving some good damage, a lot of hp, a ton of regen, and the various benefits from having stats (mana & regen, hp already mentioned, 2 armor, 15 attack speed).
I wouldn't make linkin's if I didn't need more hp (but I almost always want hp).
I wouldn't make it if I didn't need a roh or perseverence early game (but I often start my build with that, in all random).
I wouldn't make linkin's if the enemy team had no targeted spells (but does that ever happen?).
I won't make a linkin's if the game goes so poorly that farming up an ultimate orb isn't even viable before losing because the enemy team is so fed (but then the game is lost no matter what items I build, so it's irrelevant).
If I go with a lifesteal build, and don't really need any hp regen for sustain, I'd avoid going with a linkin's.
If I am playing single draft or random draft and don't get to start with the randomed gold, I'll often not build towards a linkin's just because I have to start with other sustain other than a RoH.
If the game demands a bkb, I'll build a bkb... and a linkin's. I feel the items compliment each other perfectly, do not overlap, and even the cooldown of linkin's is almost perfect to match with a bkb. you engage, linkin's blocks a spell is your signal to activate bkb, you fight, bkb runs out, and after a few more seconds linkin's is back online and ready to block something else.
If an enemy has an easily spammed nuke that can "counter" my linkin's... i'll still build it. I don't understand this argument against LS. If the enemy team is going to purposely waste a nuke that would nearly deal 200-300 damage just to put my LS on cooldown, I consider that an awesome bonus. Talk about mek being good for healing 250hp every 45 seconds, absorbing a 200+dmg nuke every 17 seconds for linkin sphere is even better.
In summary, I feel like dota items need to cover a few things- you need some regen (both hp and mana), you need some hp to avoid being burst down, you need some mana so you can cast your full range of spells without running out mid fight, and damage/armor/attack speed are all nice little bonuses. Linkin's sphere just fills all the basic needs for almost every hero, the only thing it really lacks is a good initiation like you can get from a blink dagger or force staff. It's not as much damage as a pure damage item, it's not as much hp as a heart, it's not as much magic avoidance as a bkb, and it's not as much regen as a bloodstone- but it provides all those bonuses at the same time at a cheap price all in one slot.
I like it.