You could argue the same for all testing elements if you're stubborn enough. I bet $12.32 if all that was included from the start, you would barely give mind to it.
I can tell you from experience I wouldn't enjoy it.
What was my least favorite part about Half-Life 2? Manhacks. I hated those things. They are little flying bots that hover around your space and attack you. This would be almost the same thing, except I assume it would be much slower, stay a distance and shoot a lazer at you. But what's the reason that the Manhacks work anyways, no matter how annoying they are? They're in a first person shooter, not a puzzle game. Manhacks work in HL2 because you don't ever have to solve a puzzle under the heat and pressure of flying blades all over you.
You have to think of it from a gameplay standpoint: What kind of game is Portal? It's a puzzle game. If there's some kind of bot that were to follow you around and harm you if you don't move away from it, how are you to think to your full potential if your main focus is to get out of the way/get rid of that robot? You aren't, your main focus is going to get rid of that annoying bot.
There are a couple of options Valve would have if they were to add that bot.
1. Make the puzzles very easy so you wouldn't have to think at all to solve them, just avoid the bot while doing it.
This obviously has some problems because the point of portal is to feel good when you solve a difficult challenge, not solve an easy one and feel no reward.
2. Make the puzzles normal but add a relatively simple way to get rid of the bots.
If getting rid of the bot was your main solution, what would be the point of adding the bot at all? There wouldn't be. The player is not going to experience this bot most of the time because they're just going to destroy it when they get the chance. This just adds some tedious process to your list of chamber-solving processes, and nobody likes a tedious task to deal with all the time.
3. They add the robots, there is no real good way to get rid of them efficiently and you just have to deal with them through the regular-difficulty challenges.
Same problems stated way above there ^. Nobody likes to think while being followed around and distracted by some annoying bot. It would just be frustrating to have to try and think about what they're doing while getting trolled by some floating head.
4. You almost never see the bot except occasionaly, perhaps as a deffense mechanism for GLaDOS and you more have to deal with it when escaping GLaDOS or SPOILER:
wheatley. But again, no point in adding a bot you almost never see half the time. Valve would have to train the players to use some totally different mechanic that they're only going to see occasionally.
Warning - while you were typing a new reply has been posted. You may wish to review your post. GJ marcem :)
TL;DR
Listen to the commentary. No one wants an enemy chasing them as they solve something, it's just annoying. Time pressure never works.