And I have so many answers for you!
They have murder cases every day? Yes, you are correct. They run into cases, Kogoro's pulled into cases, they hear about cases the plot is entirely revolved around cases and this is for one simple plot relevant reason: Shinichi postures himself to be the nucleus of all criminal activity in the prefecture he resides so that he can get himself closer to the Black Organization. He lives in a private detective agency: when Kogoro or Ran make reference to business being slow, they don't say they haven't had a case in weeks or months, they say days. So what we can derive from that is that on typical days they're balancing more than a single case. Cases all the time. Also we can factor in tip offs of cases from the Professor as well (to a slightly smaller degree) the Metropolitan Police and the Detective boys. So where does that leave us? Conan actively putting himself in a murder case every day. Why? Because that's the plot. I don't think that's too unreasonable!
As for the passage of time, let's decide that each episode represents a single case and that represents a 24 hour period of time. That's not the case, as the majority of the crimes are solved at the location that they're discovered in. Definitely not a whole day ordeal. Let's dislodge Anime Original episodes from the continuity, as those are openly and decidedly not canonical. That leaves us with about 435 episodes. Of those 435 episodes, 171 of them are more than 1 part. There are quite a few cases that span more, but for the benefit of the argument we'll say they're all only two parters. Nearly all of those take place in a single day, but, again, for the benefit of the argument we'll round that down to 150 for the odd duck episodes that take place for more than a 24 hour period of time. That leaves us with 285 episodes that may represent a 24 hour period. In other words, less than a year. Why have the kids not grown up? It fits perfectly within the time frame. In fact, i'll go ahead and say they do look like they've grown about a years worth of time from episode 1 to episode 696.
It's a really easy argument when you say it out loud, but I think it's a pretty trivial and cheap excuse to not watch a pretty excellent show!