are TFTs meant to be used with VGA connection?

The problem you are describing is most likely caused due to the monitor not correctly auto-aligning on its own.

This is common for any digital screen that is connected through a VGA connector.

When a screen has a VGA connector, you can count on it that the screen should look good enough to be used.

If the text is blurry and casts shadows, then it is just a sign of pixels not aligning properly. Basically the screen projects the pixel of 0,0 but because it is misaligned, it projects this on both 0,0 and 0,1 for example, and pixels blend etc.

To fix this issue, just press the AUTO button on your monitor for each monitor connected to VGA. You'll see it saying Auto-adjusting... and then the image should pop straight into the screen. Make sure you have something on screen that has no black borders. Usually anything is okay.

You have have to repeat this process for every time you switch resolution to a new resolution the first time, but the screen should remember that resolution onwards.

That said, if the screen is set to a resolution the monitor officially doesn't support or is not the native resolution, it will already try to squeeze pixels together. This will also happen on a timing issue, for exeample, if the monitor is set to 59hz instead of 60hz. Changing the hz and resolution is done in windows though. After correcting this, press auto once more.

All cables, analog or digital, have limited throughput - you can push only so much information through them per second until problems arise. "Information" here, in context of displays, means pixel color values at some resolution and refresh rate. The higher resolution and refresh rate, the more information there is to transmit.

With digital cables the throughput simply cannot be exceeded. The protocol defines valid parameter ranges and neither device will be able to break this barrier. There's a hard limit to what resolution and refresh rate combinations are possible on that link.

Analog cables are a different story. You may be able to get more out of them that they were designed for at the cost of quality. This does not mean that every receiving device will be able to work with such signal, but if both ends support it and you're okay with image deterioration, you're good.

The interesting thing about CRTs is that while their vertical resolution is discrete, the horizontal "resolution" is essentially infinite and we're using a discrete number only because it's the only practical way to handle it in a computer (TV is different). VGA's design reflects this: some signals in a VGA cable were supposed to directly drive the electron beam in a CRT. LCDs don't work like that though, they have a discrete resolution and no electron beam. The VGA signal has to be electronically sampled to recreate the discrete image the computer intended to display, and then send it to the LCD panel. While a CRT with its infinite horizontal resolution would be immune to any slight clock skew, the sampling is not, potentially degrading the quality further beyond cable's electrical limitations. This manifests as a horizontal color bleed.

With digital cables like DVI-D, HDMI and DP there's no digital-to-analog-to-digital conversion going on anymore, so you're either getting perfectly crisp image, or none at all if you're exceeding cable's capabilities.

Be careful with DVI, because there are three DVI variants that use the same cable. DVI-A is just VGA over a DVI cable, with all problems of regular VGA still there. DVI-D is 100% digital and compatible with HDMI through passive adapters. DVI-I is a mix of the two. With that last one usually only one type of signal will be used by the monitor, even though the cable carries both. Some (very old) LCDs ironically use only the analog component of DVI-I.

As to why VGA connections are still available on LCDs: because buyers sometimes still want to use them for various reasons.

tl;dr: It’s for compatibility. Use DVI if you can.

VGA connectors on displays are becoming obsolete quickly on consumer-grade flat panel displays. VGA is not suitable for 4K resolution or higher refresh rates. PCs and laptops mostly don’t have VGA connectors anymore either.

When flat panel displays were new, the opposite was true; many graphics cards, especially in office PCs, would not have digital outputs (DVI back then). That’s why cheap flat panel displays often only had VGA connectors.

When using the VGA connection with a specific source and display mode (resolution, color depth, refresh rate) for the first time, make sure to press the “Auto” button. Every flat panel display with VGA inputs has one. Make sure all edges and corners are showing bright colors, so the display can accurately measure the signal geometry.

If you can, however, you should use a digital display connection like DVI, HDMI or DisplayPort. There’s some compatibility between DVI and HDMI, too, so cheap passive adapters are available.

So yes, if you can use a DVI cable (both display and PC compatible), go for it!