What you are describing are part of the normal HPLC software performance reports generated by the popular CDS, not the MS software. MS data is different as it is based on ion counts.

Well, ion counts are principally the same as absorbance units - just some scale which we use to plot chromatographic trace. In LC-MS ion chromatograms look and behave in an absolutely the same manner as absorbance peaks with UV detector (or whatever detector is used). The only difference is that in LC-MS we simultaneously get not a single trace (as with a single wavelength in a UV detector), but a great number of traces for each m/z values which we can extract afterwards selecting as narrow m/z window for XIC as we want. It is like diode array detector which measure absorbance for the whole range of wavelength. So, the same descriptors can be applied to estimate separation quality in LC-MS analysis as in LC-UV. However, for some reason LC-MS software manufacturers do not put that much attention to this sort of analysis as in other types of chromatography detection. And this is just the problem I am having. 

I teach LC/MS operation and method development so am aware of the various MS signal plots available, but your descriptions are not entirely accurate. As long as you have collected enough MS data points across the chromatographic peak AND the sample ionizes well (not always the case in real life!), the peak shape should mirror the LC peak shape. So the tools to analyze it are usually on the LC software. Too few points and the shape by MS will be inaccurate (just like in LC). *As in LC, poor quality MS instrument settings or bad plumbing may result in misleading peak shapes.

The MS peak "shape" via TIC, SIM or whatever gathering technique or window you use is still going to be mostly a function of the separation quality achieved from the LC separation. This is why the LC software deals with these performance measurements. A secondary detector (e.g. MS) may or may not show these same shape defects, depending on how well the sample forms ions and which MS parameters/settings are used. So less importance is focused on these through the MS analysis. To some extent, we do not care as we use the MS to collect data at specific time points within a run to ID or exclude a compound. This is why it is critical to develop an excellent quality LC-MS method, not an MS method alone. Starting off with excellent chromatography methods (full separation) allows us to ADD the MS data to the initial LC detector's data (e.g. UV/VIS, RID, FLD...) and make better qualitative statements about the sample.

Quick answer: Because the typical primary HPLC detector (e.g. UV/VIS DAD) is used for the initial on-column peak separation and resolution analysis. In many cases, inline secondary detectors do not need the same tools. It would be nice if the manufacturers provided the same tools (and some do for all detectors), but you can still measure noise levels, LOD, S/N, symmetry w/o specialized tools.

I agree with all the points you mentioned. And I take it as granted that I have enough timepoint per peak to make it to somewhat normal peak shape (around 10 in my LC-MS setup). What I want is quality control for complex samples (full-cell hydrolyzates), so UV detection (even if it installed as a primary detector which nobody cares to do for nano-chromatography, since it will lead to post-column dead-volumes and to separation quality deterioration) is no help to me. I can measure peak tailing, symmetry and other parameters without specialized tools for some particular peak... but it is not so funny when one decides to do statistical distribution of these parameters across the run for multiple peaks. Or a comparison of these distributions for different sorbents. If I choose a single peak to evaluate quality of separation it might happen that this compound is better separated on one sorbent than on another. The easiest case - the sorbent (I am talking about RP separation - this is what I use) is better suited for hydrophylics and it just happened that I selected a hydrophylic peptide for quality control, while for all the rest of the chromatogram it will be worse. Yes, I can select several peaks across the run to take care of the possibility of hydrophilic-hydrophobic specialization of sorbents and make manual evaluation, but how many peptides is enough for representative comparison? And if I can measure peak parameters manually for a single compound in e.g. 8 runs (e.g. I compare 2 sorbents with 2 particle size in 2 technical repeats each) in a couple of hours, it will take days to do it manually for a dozen peaks (and not very cheering work it is:) ). So I hope to find some software that can measure these parameters automatically for XICs. And not just divide baseline-to-apex by apex-to-baseline, as e.g. Xcalibur suggests, but will make it in a proper way at 5, 10 or whatever percentage of peak height, which will be independent from peak selection parameters.

If it is possible to feed XICs to some LC analysis software - that might be a decision. If I make XIC as an intensity versus time table, I can work with it in the same way as with UV traces. However for now I cannot find a way to do this. Have you ever heard about something like this?

The later versions of Xcalibur software did allow you to calculate peak shape, but it was one of the most manually intensive setups to process signals for basic info.

BTW: 10 is usually the abs bare minimum # of points across a peak for good statistical representation and RSD. I have taught the use of at least 15 points, with 15-20 points across each peak for MS analysis (*20-30 points for LC detectors) as ideal. I would not use 10 points with an MS system... IMHO too few.

There are freeware and opensource apps which can be used to re-process data, including MS data. eXPFit is one (uses Excel) and if you look on the web, you will find others.

Most Agilent CDS (latest versions of Mass Hunter with ChemStation) packages include just about every type of peak sym and performance calculators, but as I mentioned before, some other brands are pretty basic. Waters MassLynx software has apps which can manipulate the data similar to their LC's. If your software allows export of the data into a universal format (e.g. ANDI), then you might look into exporting the data and then importing into a software package that can read and process it.