I have not read all of the replies, so I may plow the same ground as other replies.
I am a big-city night-shift LEO, myself. I have been doing it long enough to get about all of the macho-ism and adventurism out of myself. If I find an intruder inside my home, I am either going to use deadly force right then and there, or give him an out, with emphasis on the latter. The reason? Detaining someone is fraught with danger!
If I am detaining someone, I have too much attention focused on him, when he may have unseen accomplices who will attack out of the darkness, from a blind side, or his getaway driver may come to his aid, toting an AK. (Don't scoff at this third case; this seems to be a recent trend in a certain big city in Texas.) If I am moving in to apply restraints, I am even more focused on the detained bad guy, making myself more vulnerable, and of course, then have to contend with desperate moves by the primary bad guy himself.
To be clear, in the paragraph above, I am not advocating shooting without justification. It also reflects what I would do if someone broke into my home, where I am likely to be the only effective defender, and does not necessarily reflect what I would do while on the clock, when I have an obligation to detain, and "the cavalry" likely to be on the way. Giving him an out also assumes that the intruder has not yet harmed any person in my home, and will not be in a position to do harm to anyone in the family on the way out.
Regarding the police arriving on the scene while a homeowner is detaining a burglar, well, there is simply no guarantee. Here, in Texas, officers are indeed well aware that it is likely a homeowner will be armed, but there is also the very human tendency for anyone holding a gun to turn with the gun, and therefore a homeowner who is tunneled-in on the intruder may well turn with the gun in hand when first perceiving officers, and therefore be seen as a threat by those officers. An officer is going to give his own safety the benefit of the doubt. Experienced officers, with some seniority, are more likely to have been there and done that enough to be able to read the situation accurately, whereas younger and/or less-experienced officers are more likely to be too quicker on the trigger, IMHO. In the dead of night, guess which officers are more likely to be responding to a burglary-in-progress?
Detain an intruder if you wish. It is your right to do so, in Texas, at least, where the arrest powers of private citizens are very much near those of peace officers. Just be informed, and be careful.