Older models start, no prob there. Newer ones, that don't have detachable batteries, yes, they can be a problem (sometimes, depends on make and model... usually brands like Dell or Lenovo can make a fuss over it). Even in those cases, there are BIOS mods that remove this limitation.

Of course, that general advice is good and should be followed. But some batteries will die even if you follow these advices. There were some laptops back in the day that had a recharge cycle counter inside the charge/discharge controller in the battery. They would just die, out of the blue, after, let's say, 1000 charges. People that were used to having their laptops plugged in all the time, regardless if they needed that or not, spent the recharge cycles a lot faster than people that just plugged in the laptop whenever it was low on battery. This happened because the charging circuit sometimes falsely reports the battery as a little drained (99%), so it will recharge it just a tad. Still, this "just a tad" added 1 recharge cycle to the count. Over the course of a day, this may happen, 10, 15 times, which ammounts to 10, 15 charges accourding to the counter. So, their batteries basically went dead right after their warranty expired. There are ways to reset the counter or completely jump that piece of code, but it's just not worth it. Too much RCE work for very little gain.

It's a shame though... those batteries were still OK. It was just a shitty move from the manufacturers to try and squeze more money from their clients for batteries.