Part of this is implemented, although not quite in the way you suggested:
Very Low Quality and Not An Answer flags do not enter the moderator queue for 15 minutes after they're raised. This applies network-wide, except on Stack Overflow, Mathematics, TeX, Salesforce and Stack Overflow em Português (where the delay is a full hour) and meta sites (where they enter the queue immediately).
This delay gives the community a chance to handle these flags first. If that doesn't happen, or if it can't happen, then it is made available to moderators for resolution. Keep in mind, not all posts can be processed via review, and when a post is processed through review but continues to garner flags the system reserves these for moderators. Therefore, when you do see these flags in the mod queue, you should handle them - it's unlikely anyone else will.
The other two requests - declining some flags instead of disputing them, removing some auto-flags - have merit, but require some additional thought; please raise these as a separate feature-request.
Appendix: low quality handling stats, by site
The following table shows the number of review tasks created during the past 90 days, the % of those tasks successfully handled by review, and the respective median handling times, in minutes, for reviewers and moderators:
Total PctSuccessful Median review handling time Median mod handling time Site Name
----- ------------- --------------------------- ------------------------ - ---------
86850 76.92 % 34 25 * Stack Overflow
3928 33.45 % 68 48 Super User
1093 36.41 % 40 13 Server Fault
22 18.18 % 411.5 96 Stack Apps
457 20.35 % 1113 107.5 Cooking
300 55.00 % 84 32 Home Improvement
186 27.42 % 164 93 Game Developers
2419 36.17 % 115 46 Gaming
539 36.18 % 54 23 GIS
7580 83.71 % 6 23 * Mathematics
267 25.47 % 76 134 Photography
403 39.21 % 23.5 68 Statistical Analysis
465 17.20 % 161 93 Web Apps
118 56.78 % 23 21 Webmasters
1901 35.46 % 53.5 22 Apple
48 18.75 % 156 281 Theoretical Computer Science
2239 56.10 % 191.5 141 English Language and Usage
130 22.31 % 172 67.5 Personal Finance and Money
158 18.35 % 57 34 Role-playing Games
591 88.32 % 36 30 * TeX - LaTeX
4718 36.37 % 73 71 Ubuntu
1171 57.05 % 20 34 Unix and Linux
464 35.34 % 42 27 WordPress
104 20.19 % 975 221 Bicycles
810 17.16 % 98 73 Programmers
2083 13.68 % 1172 182 Android Enthusiasts
78 37.18 % 2097 2194 Board and Card Games
879 44.03 % 96 73.5 Physics
34 17.65 % 3199 3223 Homebrew
516 30.23 % 243.5 131 IT Security
38 13.16 % 727 103 Writers
539 28.01 % 37 28 Electronics and Robotics
360 39.44 % 163 136 Graphic Design
428 39.95 % 230 116 Database Administrators
736 54.21 % 93 67 Science Fiction
126 33.33 % 31.5 9 Code Review
257 66.54 % 11 113 Code Golf
70 55.71 % 151 79.5 Quantitative Finance
26 26.92 % 1179 1073.5 Project Management
131 14.50 % 163 90 Skeptics
524 41.22 % 84 51 Drupal Answers
56 10.71 % 2379 663.5 Fitness and Nutrition
174 18.39 % 462 188 Motor Vehicle Maintenance and Repair
99 10.10 % 265.5 162 Parenting
630 47.46 % 20 45 SharePoint
172 41.86 % 306 167 Musical Practice and Performance
76 21.05 % 6322.5 1062 Software Quality Assurance and Testing
221 52.49 % 89.5 92 Jewish Life and Learning
48 22.92 % 697 1202 Astronomy
147 57.82 % 37 73 German Language and Usage
52 55.77 % 110 34 Japanese Language and Usage
36 63.89 % 197 55 Gardening and Landscaping
89 13.48 % 3512.5 828.5 Philosophy
24 8.33 % 2434.5 502 Personal Productivity
327 29.05 % 134 279 Travel
113 27.43 % 1150 473 Cryptography
69 33.33 % 135 613 Signal Processing
64 53.13 % 363 132 French Language and Usage
516 6.78 % 142 93 Christianity
150 21.33 % 447.5 419 Bitcoin
40 22.50 % 464 124 Linguistics
77 1.30 % 27 3 Biblical Hermeneutics
23 21.74 % 2008 3209 Economics
128 53.91 % 247 209 History
35 20.00 % 392 377 LEGO®
94 28.72 % 4718 1323.5 Spanish Language and Usage
22 4.55 % 719 90 Computational Science
353 44.76 % 243.5 200.5 Movies
193 63.73 % 471 3708 Chinese Language and Usage
275 30.18 % 189 158.5 Biology
21 47.62 % 414.5 269.5 Poker
312 56.41 % 20 52 Mathematica
53 15.09 % 271.5 295.5 Cognitive Sciences
50 20.00 % 141 193 The Great Outdoors
25 12.00 % 2160 433.5 Martial Arts
64 37.50 % 191.5 178.5 Sports
206 33.01 % 209.5 59 Academia
133 36.09 % 141 106 Computer Science
155 21.29 % 748 322 The Workplace
214 64.49 % 514 531 Windows Phone
221 47.51 % 132 154 Chemistry
63 39.68 % 1235 1707 Chess
182 11.54 % 573 51.5 Raspberry Pi
115 60.87 % 402.5 379 Russian Language and Usage
213 11.74 % 2594 165 Islam
512 60.35 % 91 138 * Salesforce
53 35.85 % 307 464 Patents
170 21.18 % 273 64 User Experience
12 0.00 % null 238 Genealogy and Family History
23 8.70 % 6313 5049.5 Robotics
63 34.92 % 950 1049 ExpressionEngine
35 8.57 % 84 180 Politics
34 14.71 % 2644 133 Audio-Video Production
285 43.51 % 171 137.5 Anime and Manga
904 47.90 % 79 39 Magento
397 49.37 % 64 141 English Language Learners
12 41.67 % 1027 73.5 Sustainable Living
28 17.86 % 418 47 Tridion Stack Exchange
35 25.71 % 4587 1311 Reverse Engineering Stack Exchange
84 27.38 % 489 122.5 Arduino Stack Exchange
89 26.97 % 390 141 Network Engineering Stack Exchange
21 33.33 % 429 374.5 Open Data Stack Exchange
14 7.14 % 30 784 Freelancing Stack Exchange
188 47.87 % 100 103 Blender Stack Exchange
346 32.66 % 40 43 MathOverflow
84 34.52 % 95 25 Space Exploration Stack Exchange
54 20.37 % 159 92.5 Tor Stack Exchange
53 15.09 % 337.5 238 Pets Stack Exchange
25 4.00 % 214 1667 Amateur Radio Stack Exchange
19 15.79 % 166 315 Italian Language Stack Exchange
546 60.07 % 41.5 26 * Stack Overflow em Português
118 56.78 % 327 157 Aviation Stack Exchange
18 11.11 % 2046.5 853 Ebooks Stack Exchange
19 21.05 % 7112.5 1515 Beer Stack Exchange
156 14.74 % 265 153 Software Recommendations Stack Exchange
30 23.33 % 158 154 Expatriates Stack Exchange
21 28.57 % 117.5 92.5 Mathematics Educators Stack Exchange
22 22.73 % 314 221 Earth Science Stack Exchange
66 25.76 % 66 604.5 Joomla Stack Exchange
25 32.00 % 1102 656 Data Science Stack Exchange
345 44.93 % 128 77 Puzzling Stack Exchange
50 50.00 % 81 136 Craft CMS Stack Exchange
56 32.14 % 401.5 331 Buddhism Stack Exchange
43 18.60 % 85.5 49 Hinduism Stack Exchange
2 0.00 % null 88.5 Moderators Stack Exchange
23 21.74 % 251 114.5 Startups Stack Exchange
134 32.84 % 359.5 164 Worldbuilding Stack Exchange
74 28.38 % 134 70 スタック・オーバーフロー
70 50.00 % 69 64 Emacs Stack Exchange