There are voiced concerns about performance, but no data is offered. Let me suggest a simple test.
(NOTE: date on macOS does not offer nanoseconds, so this must be done on Linux.)
I have created append_test.sh on GitHub with the contents:
#!/bin/bash -e
output(){
ptime=$ctime;
ctime=$(date +%s.%N);
delta=$(bc <<<"$ctime - $ptime");
printf "%2s. %16s chars time: %s delta: %s\n" $n "$(bc <<<"10*(2^$n)")" $ctime $delta;
}
method1(){
echo 'Method: a="$a$a"'
for n in {1..32}; do a="$a$a"; output; done
}
method2(){
echo 'Method: a+="$a"'
for n in {1..32}; do a+="$a"; output; done
}
ctime=0; a="0123456789"; time method$1
Test 1:
$ ./append_test.sh 1
Method: a="$a$a"
1. 20 chars time: 1513640431.861671143 delta: 1513640431.861671143
2. 40 chars time: 1513640431.865036344 delta: .003365201
3. 80 chars time: 1513640431.868200952 delta: .003164608
4. 160 chars time: 1513640431.871273553 delta: .003072601
5. 320 chars time: 1513640431.874358253 delta: .003084700
6. 640 chars time: 1513640431.877454625 delta: .003096372
7. 1280 chars time: 1513640431.880551786 delta: .003097161
8. 2560 chars time: 1513640431.883652169 delta: .003100383
9. 5120 chars time: 1513640431.886777451 delta: .003125282
10. 10240 chars time: 1513640431.890066444 delta: .003288993
11. 20480 chars time: 1513640431.893488326 delta: .003421882
12. 40960 chars time: 1513640431.897273327 delta: .003785001
13. 81920 chars time: 1513640431.901740563 delta: .004467236
14. 163840 chars time: 1513640431.907592388 delta: .005851825
15. 327680 chars time: 1513640431.916233664 delta: .008641276
16. 655360 chars time: 1513640431.930577599 delta: .014343935
17. 1310720 chars time: 1513640431.954343112 delta: .023765513
18. 2621440 chars time: 1513640431.999438581 delta: .045095469
19. 5242880 chars time: 1513640432.086792464 delta: .087353883
20. 10485760 chars time: 1513640432.278492932 delta: .191700468
21. 20971520 chars time: 1513640432.672274631 delta: .393781699
22. 41943040 chars time: 1513640433.456406517 delta: .784131886
23. 83886080 chars time: 1513640435.012385162 delta: 1.555978645
24. 167772160 chars time: 1513640438.103865613 delta: 3.091480451
25. 335544320 chars time: 1513640444.267009677 delta: 6.163144064
./append_test.sh: fork: Cannot allocate memory
Test 2:
$ ./append_test.sh 2
Method: a+="$a"
1. 20 chars time: 1513640473.460480052 delta: 1513640473.460480052
2. 40 chars time: 1513640473.463738638 delta: .003258586
3. 80 chars time: 1513640473.466868613 delta: .003129975
4. 160 chars time: 1513640473.469948300 delta: .003079687
5. 320 chars time: 1513640473.473001255 delta: .003052955
6. 640 chars time: 1513640473.476086165 delta: .003084910
7. 1280 chars time: 1513640473.479196664 delta: .003110499
8. 2560 chars time: 1513640473.482355769 delta: .003159105
9. 5120 chars time: 1513640473.485495401 delta: .003139632
10. 10240 chars time: 1513640473.488655040 delta: .003159639
11. 20480 chars time: 1513640473.491946159 delta: .003291119
12. 40960 chars time: 1513640473.495354094 delta: .003407935
13. 81920 chars time: 1513640473.499138230 delta: .003784136
14. 163840 chars time: 1513640473.503646917 delta: .004508687
15. 327680 chars time: 1513640473.509647651 delta: .006000734
16. 655360 chars time: 1513640473.518517787 delta: .008870136
17. 1310720 chars time: 1513640473.533228130 delta: .014710343
18. 2621440 chars time: 1513640473.560111613 delta: .026883483
19. 5242880 chars time: 1513640473.606959569 delta: .046847956
20. 10485760 chars time: 1513640473.699051712 delta: .092092143
21. 20971520 chars time: 1513640473.898097661 delta: .199045949
22. 41943040 chars time: 1513640474.299620758 delta: .401523097
23. 83886080 chars time: 1513640475.092311556 delta: .792690798
24. 167772160 chars time: 1513640476.660698221 delta: 1.568386665
25. 335544320 chars time: 1513640479.776806227 delta: 3.116108006
./append_test.sh: fork: Cannot allocate memory
The errors indicate that my Bash got up to 335.54432 MB before it crashed. You could change the code from doubling the data to appending a constant to get a more granular graph and failure point. But I think this should give you enough information to decide whether you care. Personally, below 100 MB I don't. Your mileage may vary.