It has been true forever. Even the absolute very best wireless system on the market isn't as good as a $30 cable.
Two issues you have to worry about are RF range and sound quality. Cheap wireless stuff SUCKS, especially so in the analog versions. Dynamic range can be horrid, and noise floors unbearable. The companding that gets done to the signal makes mics barely usable for speech. Not something you want for singing at any level.
The function of RF is important too. Knowing the range that you really need the system to work is very important. Most wireless mic systems will advertise a working range of 300 feet, line of sight. Anyone that's worked with wireless mics will tell you that there's no chance in hell that most mics will be reliable at that sort of range.
The cheap stuff I'd plan for 50 feet outdoors, tops. That can be fine if you put the receivers on stage near the performers. Eg, a wireless guitar system may only need 10 feet of range to be effective, so there are times that short range can be fine. But, if you suddenly want to put the receivers at FOH, it's likely going to cause you issue.
Many mics now have switched to digital transmission. While this eliminates some of the issues with sound quality, especially with lower end mics, it isn't without issue. First off, digital mics add latency. All of them. Now, most of them add only a very little amount and it goes unnoticed. However, for some particular listeners, the latency of the mic, combined with the latency of the digital mixer, combined with the latency of the processor, etc can become an issue. It's more pronounced with singers that use IEMs. Secondly, like with any digital signal, making sure you don't clip the signal -EVER- is pretty important. While with analog, clipping a signal often just resulted in distortion that gradually got worse, clipping a digital signal isn't pretty, even if it's just an itty bit. Setting an appropriate gain level on the transmitter is key. I've found that cheaper mics often eliminate the ability to set gain on the transmitter where you need it to be. That can be a problem, especially when using the mic in loud situations.
Definitely, and without question, AVOID 2.4ghz mics. The problem with them is that while you may be able to test them in practice, at your event, pretty much EVERY guest in attendance is bringing a device in ther pocket that potentially can disrupt the show. No, it won't happen every time. But when it does, it's not going to be fun. Personally, I've seen the problems with 2.4ghz mics happen more often at corporate events. It's easy to explain, because there are more people there that pull out their laptops and connect to their hotspots via WIFI, saturating the space. Once saturated, the mic can't work properly.
So, back to the original question on budget. If you don't have a budget of at LEAST $500 per channel, don't consider wireless. Doing so is a waste of time and money. The guy that spent $35 on a cable will have much better sound than you.