No, it isn't.
If you're interested in the WHY, you can browse
the forums here as this has been discussed several times.

I don't see much point.....even in console emulators I don't much see the point.

State saving is great in console emulators because many old games didn't have a save/continue feature but were very long and/or difficult to beat. It's also nice to be able to save at any point during gameplay instead of just at save points or when you die or whatever.

In the case of DOSBox, I'm not sure the effort required to implement this would be worth it in the end, since the availability of writable media means that the vast majority of PC games allow you to save your progress. It would probably be most useful for really old games like booters and whatnot.

In most console emulators there is a point - that of convenience. Consoles mostly work with savepoints, or whatever to call them. For example in Zelda for N64 you can save at what point you will but if you have to reload you are at the beginning of the level again. This is mostly not to workaround a console limitation but just there to have the games seem longer to take to play through.
PC games mostly work in the way that you can save wherever you want and when you reload you start right where you saved.
Thankfully most emulators allow the PC like saving.

Edit: I started to write this before HunterZ' reply was there 😀

Well when I play console games I only save where I am meant to....because it just seems like cheating otherwise. The only games I ever use state saves in are old NES games that use passwords. However I only save it in areas where you can get the passcode and not just when I feel like it.

I guess for me I like to play the way it was meant to be played...

For me, part of the fun of using emulators is to have an enhanced experience. This may be due to graphic filters/scalers, support for modern controllers, state saving, and often straight-up cheating features. Mostly I use state saving for convenience - allowing me to simulate a straight play-through of the game without turning it off or manually saving, but it's often useful for relievining the frustration that comes with playing some old games that would take me forever to beat otherwise (either due to length or difficulty).

I'm not really a fan of filters.....give me pixelated goodness any day! 😁 Nostalgia I guess....

Exactly...and this is what forums debate on. I personally believe in story as being the primary focus, therefore anything that helps me to be interested in the story and anything to help further that purpose is up for grabs. (Save States, Save Anywhere, Walkthroughs). I'll try to play the game the "way it was intended" (whatever the hell that means) as much as possible but as soon as craptacular game programming and imposed limitations comes into effect, I'll do whatever it takes to progress further even if it involves cheating.

I think it has to do with a person's personality. I'm not a competitive person, I don't like sports, I don't like MMORPG's (No story), (Although I do like MUDDS....simple because there is more story), basically anything that is competitive I don't like unless I'm playing a LAN/House party gaming and then I'll play for fun. Basically, I'm not the type of person who like's to brag about how he restarted a level 50 damn times to finish a game.

About the "pixelated goodness": Part of my problem with that (especially in regards to emulating console games) is that my 21" CRT is much better quality than the display devices used when the games were new, so playing without a filter can in my opinion be a worse experience than would be playing on whatever quality of display device you originally had at the time the game was new. As a result, most of what I use scalers/filters for is to actually make things blurrier so that they'll be closer to the original experience.

I can think of two exceptions:
1. 3D games that used to be software-rendered but now have hardware-accelerated ports or emulators (e.g. Doom 1 & 2, Quake 1, PSX). For me, these are all about running in super high-res with FSAA cranked up and using mouselook in games that were designed for keyboard play 😀

2. SCUMMVM. It has some nice scalers with intelligent interpolation that do a decent job of making 320x200 games look like they were designed for 640x480, if not higher.

I'm just rambling now - pay no attention 😜